Discrete mathematics Books

Book SynopsisThis textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.Table of ContentsPreface.- List of Algorithms.- List of Bibliographical Notes.- Part 1. Topics in network optimisation.- 1. An introduction to graphs.- 2. Graph connectedness.- 3. Algorithmic complexity.- 4. Optimal paths.- 5. Trees.- 6. Location problems.- 7. Maximum flow networks.- 8. Minimum-cost network flows.- Part 2. Topics in classical graph theory.- 9. Matchings.- 10. Eulerian graphs.- 11. Hamiltonian graphs.- 12. Graph connectivity.- 13. Planarity.- 14. Graph colouring.- 15. Oriented graphs. Part 3. Topics in modern graph theory.- 16. Domination in graphs.- 17. Ramsey Theory.- 18. Extremal graph theory.- 19. Graph enumeration.- 20. The probabilistic method.- Index.

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Book SynopsisThis proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020. The SEICCGTC is broadly considered to be a trendsetter for other conferences around the world – many of the ideas and themes first discussed at it have subsequently been explored at other conferences and symposia.The conference has been held annually since 1970, in Baton Rouge, Louisiana and Boca Raton, Florida. Over the years, it has grown to become the major annual conference in its fields, and plays a major role in disseminating results and in fostering collaborative work.This volume is intended for the community of pure and applied mathematicians, in academia, industry and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields.Table of ContentsRatio Balancing Numbers(Bartz et al).- An Unexpected Digit Permutation from Multiplying in any Number Base(Qu et al).- A & Z Sequences for Double Riordan Arrays (Branch et al).- Constructing Clifford Algebras for Windmill and Dutch Windmill Graphs; A New Proof of The Friendship Theorem(Myers).- Finding Exact Values of a Character Sum (Peart et al).- On Minimum Index Stanton 4-cycle Designs (Bunge et al).- k-Plane Matroids and Whiteley’s Flattening Conjectures (Servatius et al).- Bounding the edge cover of a hypergraph (Shahrokhi).- A Generalization on Neighborhood Representatives (Holliday).- Harmonious Labelings of Disconnected Graphs involving Cycles and Multiple Components Consisting of Starlike Trees(Abueida et al).- On Rainbow Mean Colorings of Trees (Hallas et al).- Examples of Edge Critical Graphs in Peg Solitaire (Beeler et al).- Regular Tournaments with Minimum Split Domination Number and Cycle Extendability (Factor et al).- Independence and Domination of Chess Pieces on Triangular Boards and on the Surface of a Tetrahedron(Munger et al).- Efficient and Non-efficient Domination of Z-stacked Archimedean Lattices (Paskowitz et al).- On subdivision graphs which are 2-steps Hamiltonian graphs and hereditary non 2-steps Hamiltonian graphs (Lee et al).- On the Erd}os-S_os Conjecture for graphs with circumference at most k + 1 (Heissan et al).- Regular graph and some vertex-deleted subgraph (Egawa et al).- Connectivity and Extendability in Digraphs (Beasle).-On the extraconnectivity of arrangement graphs (Cheng et al).- k-Paths of k-Trees(Bickle).-Rearrangement of the Simple Random Walk(Skyers et al).- On the Energy of Transposition Graphs(DeDeo).- A Smaller Upper Bound for the (4; 82) Lattice Site Percolation Threshold(Wierman).

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Book SynopsisThis book constitutes the refereed proceedings of the 15th International Conference on Graph Transformation, ICGT 2022, which took place Nantes, France in July 2022.The 10 full papers and 1 tool paper presented in this book were carefully reviewed and selected from 19 submissions. The conference focuses on describing new unpublished contributions in the theory and applications of graph transformation as well as tool presentation papers that demonstrate main new features and functionalities of graph-based tools.Table of ContentsTheoretical Advances.- Application Domains.- Tool Presentation.

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Book SynopsisThis book constitutes the proceedings of the 16th International Conference on Algorithmic Aspects in Information and Management, AAIM 2022, which was held online during August 13-14, 2022. The conference was originally planned to take place in Guangzhou, China, but changed to a virtual event due to the COVID-19 pandemic.The 41 regular papers included in this book were carefully reviewed and selected from 59 submissions. Table of ContentsAn improvement of the bound on the odd chromatic number of 1-planar graphs.- AoI Minimizing of Wireless Rechargeable Sensor Network based on Trajectory Optimization of Laser-Charged UAV.- Monotone k-Submodular Knapsack Maximization: An Analysis of the Greedy+Singleton Algorithm.- The constrained parallel-machine scheduling problem with divisible processing times and penalties.- Energy-constrained Geometric Covering Problem.- Fast searching on $k$-combinable graphs.- Three Algorithms for Converting Control Flow Statements from Python to XD-M.- Class Ramsey numbers involving induced graphs.- An Approximation Algorithm for the Clustered Path Travelling Salesman Problem.- Hyperspectral Image Reconstruction for SD-CASSI systems based on Residual Attention Network.- Improved Approximation Algorithm for the Asymmetric Prize-Collecting TSP.- Injective edge coloring of power graphs and necklaces.- Guarantees for Maximization of $k$-Submodular Functions with a Knapsack and a Matroid Constraint.- Incremental SDN Deployment to Achieve Load Balance in ISP Networks.- Approximation scheme for single-machine rescheduling with job delay and rejection.- Defense of Scapegoating Attack in Network Tomography.- A Binary Search Double Greedy Algorithm for Non-monotone DR-submodular Maximization.- Streaming Adaptive Submodular Maximization.- Constrained Stochastic Submodular Maximization with State-Dependent Costs.- Online early work maximization problem on two hierarchical machines with buffer or rearrangements.- Polynomial time algorithm for k-vertex-edge dominating problem in interval graphs.- Adaptive Competition-based Diversified-profit Maximization with Online Seed Allocation.- Collaborative Service Caching in Mobile Edge Nodes.- A Decentralized Auction Framework with Privacy Protection in Mobile Crowdsourcing.- On-line single machine scheduling with release dates and submodular rejection penalties.- Obnoxious Facility Location Games with Candidate Locations.- Profit Maximization for Multiple Products in Community-based Social Networks.- MCM: A Robust Map Matching Method by Tracking Multiple Road Candidates.- Security on Ethereum: Ponzi Scheme Detection in Smart Contract.- Cyclically orderable generalized Petersen graphs.- The r-dynamic chromatic number of planar graphs without special short cycles.- Distance Labeling of the Halved Folded $n$-Cube.- Signed network embedding based on muti-attention mechanism.- Balanced Graph Partitioning based on Mixed 0-1 Linear Programming and Iteration Vertex Relocation Algorithm.- Partial inverse min-max spanning tree problem under the weighted bottleneck Hamming distance.- Mixed Metric Dimension of Some Plane Graphs.- The Optimal Dynamic Rationing Policy in the Stock-Rationing Queue.- Pilot Pattern Design with Branch and Bound in PSA-OFDM System.- Bicriteria Algorithms for Maximizing the Difference Between Submodular Function and Linear Function under Noise.- On the Transversal Number of k-Uniform Connected Hypergraphs.- Total coloring of planar graphs without some adjacent cycles.

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Book SynopsisThis textbook aims to point out the most important principles of data analysis from the mathematical point of view. Specifically, it selected these questions for exploring: Which are the principles necessary to understand the implications of an application, and which are necessary to understand the conditions for the success of methods used? Theory is presented only to the degree necessary to apply it properly, striving for the balance between excessive complexity and oversimplification. Its primary focus is on principles crucial for application success. Topics and features: Focuses on approaches supported by mathematical arguments, rather than sole computing experiences Investigates conditions under which numerical algorithms used in data science operate, and what performance can be expected from them Considers key data science problems: problem formulation including optimality measure; learning and generalization in relationships to training set size and number of free parameters; and convergence of numerical algorithms Examines original mathematical disciplines (statistics, numerical mathematics, system theory) as they are specifically relevant to a given problem Addresses the trade-off between model size and volume of data available for its identification and its consequences for model parametrization Investigates the mathematical principles involves with natural language processing and computer vision Keeps subject coverage intentionally compact, focusing on key issues of each topic to encourage full comprehension of the entire book Although this core textbook aims directly at students of computer science and/or data science, it will be of real appeal, too, to researchers in the field who want to gain a proper understanding of the mathematical foundations “beyond” the sole computing experience.Table of Contents1. Data Science and its Tasks.- 2. Application Specific Mappings and Measuring the Fit to Data.- 3. Data Processing by Neural Networks.- 4. Learning and Generalization.- 5. Numerical Algorithms for Network Learning.- 6. Specific Problems of Natural Language Processing.- 7. Specific Problems of Computer Vision.

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Book SynopsisGenerating function (GF) is a mathematical technique to concisely represent a known ordered sequence into a simple continuous algebraic function in dummy variable(s). This Second Edition introduces commonly encountered generating functions (GFs) in engineering and applied sciences, such as ordinary GF (OGF), exponential GF (EGF), as also Dirichlet GF (DGF), Lambert GF (LGF), Logarithmic GF (LogGF), Hurwitz GF (HGF), Mittag-Lefler GF (MLGF), etc. This book is intended mainly for beginners in applied science and engineering fields to help them understand single-variable GFs and illustrate how to apply them in various practical problems. Specifically, the book discusses probability GFs (PGF), moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), survival function GFs (SFGF), rising and falling factorial GFs, factorial moment, and inverse factorial moment GFs. Applications of GFs in algebra, analysis of algorithms, bioinformatics, combinatorics, economics, finance, genomics, geometry, graph theory, management, number theory, polymer chemistry, reliability, statistics and structural engineering have been added to this new edition. This book is written in such a way that readers who do not have prior knowledge of the topic can easily follow through the chapters and apply the lessons learned in their respective disciplines.Table of ContentsTypes of Generating Functions.- Operations on Generating Functions.- Generating Functions in Statistics.- Applications of Generating Functions.- Bibliography.

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Book SynopsisThis book provides an elementary introduction, complete with detailed proofs, to the celebrated tilings of the plane discovered by Sir Roger Penrose in the '70s. Quasi-periodic tilings of the plane, of which Penrose tilings are the most famous example, started as recreational mathematics and soon attracted the interest of scientists for their possible application in the description of quasi-crystals. The purpose of this survey, illustrated with more than 200 figures, is to introduce the curious reader to this beautiful topic and be a reference for some proofs that are not easy to find in the literature. The volume covers many aspects of Penrose tilings, including the study, from the point of view of Connes' Noncommutative Geometry, of the space parameterizing these tilings.Table of ContentsIntroduction.- Tilings and puzzles.- Robinson triangles.- Penrose tilings.- De Bruijn’s pentagrids.- The noncommutative space of Penrose tilings.-Some useful formulas.

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Book SynopsisThis book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. “Safe” – that is, paradox-free – informal set theory is introduced following on the heels of Russell’s Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor’s diagonalisation technique. Predicate logic “for the user” is introduced along with axioms and rules and extensive examples. Partial orders and the minimal condition are studied in detail with the latter shown to be equivalent to the induction principle. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of functions and sets. Techniques for solving recurrence relations including generating functions, the O- and o-notations, and trees are provided. Over 200 end of chapter exercises are included to further aid in the understanding and applications of discrete mathematics. Table of ContentsElementary Informal Set Theory.- Safe Set Theory.- Relations and Functions.- A Tiny Bit of Informal Logic.- Inductively Defined Sets and Structural Induction.- Recurrence Equations.- Trees and Graphs.

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Book SynopsisThis book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21–23, 2023. The 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.

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Book SynopsisThis volume constitutes the proceedings of the 9th International Conference on Variable Neighborhood Search, ICVNS 2023, held in Abu Dhabi, United Arab Emirates, in October 2022.The 11 full papers presented in this volume were carefully reviewed and selected from 29 submissions. The papers describe recent advances in methods and applications of variable neighborhood search.Table of ContentsA metaheuristic approach for solving Monitor Placement Problem.- A VNS-based heuristic for the minimum number of resources under a perfect schedule.- BVNS for Overlapping Community Detection.- A Simulation-Based Variable Neighborhood Search Approach for Optimizing Cross-Training Policies.- Multi-Objective Variable Neighborhood Search for improving software modularity.- An Effective VNS for Delivery Districting.- BVNS for the Minimum Sitting Arrangement problem in a cycle.- Assigning Multi-Skill Confgurations to Multiple Servers with a Reduced VNS.- Multi-Round Infuence Maximization: A Variable Neighborhood Search Approach.- A VNS based heuristic for a 2D Open Dimension Problem.- BVNS for the bi-objective multi row equal facility layout problem.

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Book SynopsisThis book constitutes the refereed proceedings of the 17th International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom (IJTCS-FAW 2023), consisting of the 17th International Conference on Frontier of Algorithmic Wisdom (FAW) and the 4th International Joint Conference on Theoretical Computer Science (IJTCS), held in Macau, China, during August 14–18, 2023.FAW started as the Frontiers of Algorithmic Workshop in 2007 at Lanzhou, China, and was held annually from 2007 to 2021 and published archival proceedings. IJTCS, the International joint theoretical Computer Science Conference, started in 2020, aimed to bring in presentations covering active topics in selected tracks in theoretical computer science. To accommodate the diversified new research directions in theoretical computer science, FAW and IJTCS joined their forces together to organize an event for information exchange of new findings and work of enduring value in the field. The 21 full papers included in this book were carefully reviewed and selected from 34 submissions. They were organized in topical sections as follows: algorithmic game theory; algorithms and data structures; combinatorial optimization; and computational economics.Table of ContentsUnderstanding the Relationship Between Core Constraints and Core-Selecting Payment Rules in Combinatorial Auctions.- An Improved Analysis of the Greedy+Singleton Algorithm for k-Submodular Knapsack Maximization.- Generalized Sorting with Predictions Revisited.- Eliciting Truthful Reports with Partial Signals in Repeated Games.- On the NP-hardness of two scheduling problems under linear constraints.- On the Matching Number of k-Uniform Connected Hypergraphs with Maximum Degree.- Max-Min Greedy Matching Problem: Hardness for the Adversary and Fractional Variant.- Approximate Core Allocations for Edge Cover Games.- Random Approximation Algorithms for Monotone k-Submodular Function Maximization with Size Constraints.- Additive Approximation Algorithms for Sliding Puzzle.- Differential Game Analysis for Cooperation Models in Automotive Supply Chain under Low-Carbon Emission Reduction Policies.- Adaptivity Gap for Influence Maximization with Linear Threshold Model on Trees.- Physically Verifying the First Nonzero Term in a Sequence: Physical ZKPs for ABC End View and Goishi Hiroi.- Mechanism Design in Fair Sequencing.- Red-Blue Rectangular Annulus Cover Problem.- Applying Johnson's Rule in Scheduling Multiple Parallel Two-Stage Flowshops.- The Fair k-Center with Outliers Problem: FPT and Polynomial Approximations.- Constrained Graph Searching on Trees.- EFX Allocations Exist for Binary Valuations.- Maximize Egalitarian Welfare for Cake Cutting.- Stackelberg Strategies on Epidemic Containment Games.

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Book SynopsisThis book provides a comprehensive algebraic treatment of hypergroups, as defined by F. Marty in 1934. It starts with structural results, which are developed along the lines of the structure theory of groups. The focus then turns to a number of concrete classes of hypergroups with small parameters, and continues with a closer look at the role of involutions (modeled after the definition of group-theoretic involutions) within the theory of hypergroups. Hypergroups generated by involutions lead to the exchange condition (a genuine generalization of the group-theoretic exchange condition), and this condition defines the so-called Coxeter hypergroups. Coxeter hypergroups can be treated in a similar way to Coxeter groups. On the other hand, their regular actions are mathematically equivalent to buildings (in the sense of Jacques Tits). A similar equivalence is discussed for twin buildings. The primary audience for the monograph will be researchers working in Algebra and/or Algebraic Combinatorics, in particular on association schemes.Table of Contents1 Basic Facts : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11.1 Neutral Elements and Inverse Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Complex Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Thin Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5 Groups and Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.6 Actions of Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.7 Hypergroups Admitting Regular Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.8 Association Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Closed Subsets : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 272.1 Basic Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2 Dedekind Modularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.3 Generating Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4 Commutators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.5 Conjugation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.6 The Thin Radical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.7 Foldings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Elementary Structure Theory: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 473.1 Centralizers and Normalizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Su cient Conditions for Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.3 Strong Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.4 Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.5 Computations in Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.6 Homomorphisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.7 The Homomorphism Theorem and the Isomorphism Theorems . . . . . . . . . . 714 Subnormality and Thin Residues : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 794.1 Subnormal Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.2 Composition Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.3 The Thin Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.4 Thin Residues of Thin Residues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.5 Residually Thin Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.6 Finite Residually Thin Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.7 Solvable Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045 Tight Hypergroups : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1075.1 Tight Hypergroup Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.2 The Set S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.3 The Sets a b \ Fc and Sa;b(Fc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.4 The Sets bf1b  \ Fa and Sb;(f1;:::;fn)(Fa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175.5 Structure Constants of Finite Tight Hypergroups . . . . . . . . . . . . . . . . . . . . . 1225.6 Rings Arising from Certain Finite Tight Hypergroups . . . . . . . . . . . . . . . . . 1265.7 Finite Metathin Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.8 Finite Metathin Hypergroups with Restricted Thin Residue . . . . . . . . . . . . 1326 Involutions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1376.1 Basic Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1386.2 Cosets of Closed Subsets Generated by an Involution, I . . . . . . . . . . . . . . . . 1426.3 Cosets of Closed Subsets Generated by an Involution, II . . . . . . . . . . . . . . . 1456.4 Cosets of Closed Subsets Generated by an Involution, III . . . . . . . . . . . . . . . 1476.5 Length Functions De ned by Sets of Involutions . . . . . . . . . . . . . . . . . . . . . . 1526.6 Hypergroups Generated by Two Distinct Involutions . . . . . . . . . . . . . . . . . . 1566.7 Dichotomy and the Exchange Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1616.8 Projective Hypergroups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1647 Hypergroups with a Small Number of Elements : : : : : : : : : : : : : : : : : : : : : : 1717.1 Hypergroups of Cardinality at Most 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1727.2 Non-Symmetric Hypergroups of Cardinality 4 . . . . . . . . . . . . . . . . . . . . . . . . 1797.3 Hypergroups of Cardinality 6 with a Non-Normal Closed Subset, I . . . . . . 1907.4 Hypergroups of Cardinality 6 with a Non-Normal Closed Subset, II . . . . . . 2027.5 Non-Normal Closed Subsets Missing Four Elements . . . . . . . . . . . . . . . . . . . 2157.6 Non-Normal Closed Subsets Missing Four Elements and Thin Elements . . 2218 Constrained Sets of Involutions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2238.1 Basic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2248.2 Constrained Sets of Involutions and Cosets . . . . . . . . . . . . . . . . . . . . . . . . . . . 2288.3 Constrained Sets of Involutions and the Thin Radical . . . . . . . . . . . . . . . . . . 2308.4 Constrained Sets of Involutions and Dichotomy . . . . . . . . . . . . . . . . . . . . . . . 2338.5 Constrained Sets of Non-Thin Involutions and Dichotomy . . . . . . . . . . . . . . 2398.6 Constrained Sets of Involutions and Foldings . . . . . . . . . . . . . . . . . . . . . . . . . 2448.7 Dichotomic Constrained Sets of Involutions and Foldings . . . . . . . . . . . . . . . 2489 Coxeter Sets of Involutions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2519.1 General Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2529.2 The Sets V1(U) for Subsets U of Coxeter Sets V of Involutions . . . . . . . . . . 2569.3 The Sets V����1(U) for Subsets U of Coxeter Sets V of Involutions . . . . . . . . . 2639.4 Sets of Subsets of Coxeter Sets of Involutions . . . . . . . . . . . . . . . . . . . . . . . . . 2659.5 Spherical Coxeter Sets of Involutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2689.6 Subsets of Spherical Coxeter Sets of Involutions . . . . . . . . . . . . . . . . . . . . . . . 2739.7 Coxeter Sets of Involutions and Foldings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2779.8 Coxeter Sets of Involutions and Their Coxeter Numbers . . . . . . . . . . . . . . . . 2809.9 Coxeter Sets of Involutions and Type Preserving Bijections . . . . . . . . . . . . . 28610 Regular Actions of (Twin) Coxeter Hypergroups: : : : : : : : : : : : : : : : : : : : : 29310.1 Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29310.2 Twin Buildings, I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29810.3 Twin Buildings, II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30110.4 Regular Actions of Coxeter Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30510.5 Regular Actions of Twin Coxeter Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . 315References : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 333

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Book SynopsisThis volume constitutes the thoroughly refereed proceedings of the 49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023. The 33 full papers presented in this volume were carefully reviewed and selected from a total of 116 submissions. The WG 2022 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science, or by extracting new graph theoretic problems from applications.Table of ContentsProportionally Fair Matching with Multiple Groups.- Reconstructing Graphs from Connected Triples.- Parameterized Complexity of Vertex Splitting to Pathwidth at most 1.- Odd Chromatic Number of Graph Classes.- Deciding the Erdos-P osa property in 3-connected digraphs.- New Width Parameters for Independent Set: One-sided-mim-width and Neighbor-depth.- Computational Complexity of Covering Colored Mixed Multigraphswith Degree Partition Equivalence Classes of Size at Most Two.- Cutting Barnette graphs perfectly is hard.- Metric dimension parameterized by treewidth in chordal graphs.- Efficient Constructions for the Gyori-Lovasz Theorem on Almost Chordal Graphs.- Generating faster algorithms for d-Path Vertex Cover.- A new width parameter of graphs based on edge cuts: -edge-crossing width.- Snakes and Ladders: a Treewidth Story.- Parameterized Results on Acyclic Matchings with Implications for Related Problems.- P-matchings Parameterized by Treewidth.- Algorithms and hardness for Metric Dimension on digraphs.- Degreewidth : a New Parameter for Solving Problems on Tournaments.- Approximating Bin Packing with Con ict Graphs via Maximization Techniques.- i-Metric Graphs: Radius, Diameter and all Eccentricities.- Maximum edge colouring problem on graphs that exclude a xed minor.- Bounds on Functionality and Symmetric Di erence { Two Intriguing Graph Parameters.- Cops and Robbers on Multi-layer Graphs.- Parameterized Complexity of Broadcasting in Graphs.- Turan's Theorem Through Algorithmic Lens.- On the Frank number and nowhere-zero ows on graphs.- On the minimum number of arcs in 4-dicritical oriented graphs.- Tight Algorithms for Connectivity Problems Parameterized byModular-Treewidth.

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Book SynopsisThis book constitutes the proceedings of the 49th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2024, held in Cochem, Germany, in February 2024. The 33 full papers presented in this book were carefully reviewed and selected from 81 submissions. The book also contains one invited talk in full paper length. They focus on original research and challenges in foundations of computer science including algorithms, AI-based methods, computational complexity, and formal models.Table of ContentsThe Information Extraction Framework of Document Spanners - A Very Informal Survey.- Generalized Distance Polymatrix Games.- Relaxed agreement forests.- On the Computational Complexity of Generalized Common Shape Puzzles.- Fractional Bamboo Trimming and Distributed Windows Scheduling.- New support size bounds and proximity bounds for integer linear programming.- On the Parameterized Complexity of Minus Domination.- Exact and Parameterized Algorithms for Choosability.- Parameterized Algorithms for Covering by Arithmetic Progressions.- Row-column combination of Dyck words.- Group Testing in Arbitrary Hypergraphs and Related Combinatorial Structures.- On the parameterized complexity of the Perfect Phylogeny problem.- Data reduction for directed feedback vertex set on graphs without long induced cycles.- Visualization of Bipartite Graphs in Limited Window Size.- Outerplanar and Forest Storyplans.- The Complexity of Cluster Vertex Splitting and Company.- Morphing Graph Drawings in the Presence of Point Obstacles.- Word-Representable Graphs from a Word’s Perspective.- Removable Online Knapsack with Bounded Size Items.- The Complexity of Online Graph Games.- Faster Winner Determination Algorithms for (Colored) Arc Kayles.- Automata Classes Accepting Languages Whose Commutative Closure is Regular.- Shortest Characteristic Factors of a Deterministic Finite Automaton and Computing Its Positive Position Run by Pattern Set Matching.- Query Learning of Minimal Deterministic Symbolic Finite Automata Separating Regular Languages.- Apportionment with Thresholds: Strategic Campaigns Are Easy in the Top-Choice But Hard in the Second-Chance Mode.- Local Certification of Majority Dynamics.- Complexity of Spherical Equations in Finite Groups.- Positive Characteristic Sets for Relational Pattern Languages.- Algorithms and Turing Kernels for Detecting and Counting Small Patterns in Unit Disk Graphs.- The Weighted HOM-Problem over Fields.- Combinatorics of block-parallel automata networks.- On the piecewise complexity of words and periodic words.- Distance Labeling for Families of Cycles.- On the induced problem for fixed-template CSPs.

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Book Synopsis- Mathematics and computer science in the information revolution.- NLP and some research results in Senegal.- On absolute valued algebras with nonzero central element.- On algebraic algebras without divisors of zero satisfying (xp, xq, xr) = 0.- Computing minimal free resolutions over monomial semirings with coefficients in D-A rings.- Schur complement and inequalities of eigenvalues on block Hadamard product.- A perturbed Mann-type algorithm for zeros of maximal monotone mappings.- On Rickart and Baer semimodules.- Completion fractions modules of filtered modules over non-necessarily commutative filtered rings.- On S-lifting semimodules over semirings.- A contribution to the study of a class of noncommutative ideals admitting finite Gröbner bases.- Construction of numbers with the same normality properties as a given number. - Robustness of imputation methods with backpropagation algorithm in nonlinear multiple regression.- A better random forest classifier: Labels guided Mondrian forest.- Remote sensing of artisanal mines buried in the ground by infrared thermography using UAV.- Implementation of EdDSA in the Ethereum blockchain.- Vulnerability prediction of web applications from source code based on machine learning and deep learning: Where are we at?.- Business process management and process mining on the large: Overview, challenges and research directions.

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Book SynopsisThe starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the non-stationary ideal on ω1; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universal-existential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method. This monograph is directed to researchers and advanced graduate students in Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of Ω-logic and related matters.

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Book SynopsisThis monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas.The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties.Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.Trade Review“This book provides a current survey of techniques and applications of symmetric functions to enumeration theory, with emphasis on the combinatorics of the transition matrices between bases. … Each chapter ends with a substantial number of exercises along with full solutions, as well as accurate bibliographic notes. The book is definitely a very interesting addition to the literature on the subject.” (Domenico Senato, Mathematical Reviews, February, 2017)“Though the authors target graduate students, advanced undergraduates will also surely have the necessary prerequisites, easily grasp the book's goals, and find many chapters accessible. … Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (D. V. Feldman, Choice, Vol. 53 (12), September, 2016)Table of ContentsPreface.- Permutations, Partitions, and Power Series.- Symmetric Functions.- Counting with the Elementary and Homogeneous.- Counting with a Nonstandard Basis.- Counting with RSK.- Counting Problems that Involve Symmetry.- Consecutive Patterns.- The Reciprocity Method.- Appendix: Transition Matrices.- References.- Index.

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Book SynopsisThis book is an elegant and rigorous presentation of integer programming, exposing the subject’s mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the reader’s understanding and serving as a gateway to deeper study.Key topics include: formulations polyhedral theory cutting planes decomposition enumeration semidefinite relaxations Written by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.Trade Review“Integer Programming begins by introducing the subject and giving several examples of integer programming problems. … This book would be suitable for a graduate level course on the mathematics of cutting plane methods. … This book might also be of interest as a reference for researchers working in this area. … This book offers a more focused presentation that makes it better suited for use as a textbook.” (Brian Borchers, MAA Reviews, maa.org, December, 2015)“The book is written in a very clear and didactic style. … very useful for mathematically mature undergraduates, graduate students, postdocs, and established researchers who are interested in the techniques. …This is an excellent and impressive book. We wholeheartedly recommend it as a textbook for advanced undergraduate and introductory graduate courses on integer programming.” (Jakub Marecek, Interfaces, Vol. 45 (5), September-October, 2015)“The authors deliver a comprehensive presentation of integer programming. … Everything is presented in a rigorous way, but on the other hand, the form makes it easy to understand for everyone. Each chapter is followed by the exercises, that allow to recall the contents. … the book is an essential text in the field of integer programing, that should be recommended as a very useful textbook for students, but also a valuable introduction for the researchers in this area.” (Marcin Anholcer, zbMATH 1307.90001, 2015)Table of ContentsPreface.- 1 Getting Started.- 2 Integer Programming Models.- 3 Linear Inequalities and Polyhedra.- 4 Perfect Formulations.- 5 Split and Gomory Inequalities.- 6 Intersection Cuts and Corner Polyhedra.- 7 Valid Inequalities for Structured Integer Programs.- 8 Reformulations and Relaxations.- 9 Enumeration.- 10 Semidefinite Bounds.- Bibliography.- Index.

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Book SynopsisThis book is intended as a teacher’s manual and as an independent-study handbook for students and mathematical competitors. Based on a traditional teaching philosophy and a non-traditional writing approach (the stair-step method), this book consists of new problems with solutions created by the authors. The main idea of this approach is to start from relatively easy problems and “step-by-step” increase the level of difficulty toward effectively maximizing students' learning potential. In addition to providing solutions, a separate table of answers is also given at the end of the book. A broad view of mathematics is covered, well beyond the typical elementary level, by providing more in depth treatment of Geometry and Trigonometry, Number Theory, Algebra, Calculus, and Combinatorics.Trade Review“This book is original, enticing, and highly stimulating, and it is a useful addition to the competition-oriented literature.” (Stephen Rout, The Mathematical Gazette, Vol. 104 (560), July, 2020)Table of ContentsGeometry and Trigonometry.- Number Theory.- Algebra.- Calculus.- Combinatorics.- Hints.- Solutions.- Answers.

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Book SynopsisDas Buch stellt wesentliche Ansätze, Ergebnisse und Methoden der linearen und ganzzahligen Optimierung dar. Ziel ist es, eine solide mathematische Grundlage des Gebietes und seiner wichtigsten algorithmischen Ansätze zu entwickeln. Methodisch zentral ist der geometrische Zugang.Table of ContentsEinleitung. - Einstiege: Ungleichungssysteme und diskrete Strukturen. - Einstiege: Algorithmen und Komplexität. - Konvexitätstheorie - Der Simplex-Algorithmus. - LP-Dualität.

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Book SynopsisThis introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Möbius functions.Table of Contents1. Introduction and Overview.- 2. Preliminaries.- 3.Bonferroni Inequalities via Abstract Tubes.- 4. Abstract Tubes via Closure and Kernel Operators.- 5. Recursive Schemes.- 6. Reliability Applications.- 7. Combinatorial Applications and Related Topics.- Bibliography.- Index.

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Book SynopsisInterview.- Mathematische Konzepte in der Finanzwirtschaft und deren Anwendung.- Kombinatorik: Die Kunst, "alles auf einen Blick zu erkennen.

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Book SynopsisQuesto breve libro propone con uno spirito via via d’immagine storiografica e di dettaglio matematico, la nascita e l’evoluzione del concetto di curvatura: le sue origini ancestrali nella meccanica, nell’astronomia, nella geodesia, e infine, chiaramente nella geometria. Gli aspetti tecnici, a volte estremamente semplici, altre volte complessi, sono sempre accompagnati da spiegazioni che si sperano esaurienti.È ben noto che su entrambi i versanti culturali proposti nel libro, molto si è scritto e ad altissimo livello; qui, c’è un tentativo di sintesi, della storiografia e della matematica sul tema della curvatura. Il racconto del filo che intercorre tra Huygens, Gauss, Riemann, Christoffel, Ricci Curbastro, Levi-Civita e infine Einstein, è stato sicuramente già ben proposto sul versante puramente storico o in quello prettamente matematico: è una speranza che la narrazione qui presentata, con questi punti di vista intrecciati, sia infine soddisfacente. Il tentativo andava fatto. L’augurio forte è che gli argomenti narrati risultino coinvolgenti per il lettore, spingendolo ad esplorare autonomamente altri aspetti magari nascosti nelle pieghe della nozione di curvatura e del mondo che ci vive attorno. Il volume muove inizialmente dal racconto di qualche frammento di cosmologia antica e medioevale. Tutto ciò è solo apparentemente estraneo al corpo vivo della materia: ritroveremo per esempio che la concezione cosmologica di Dante, riassunta qui matematicamente, propose un universo come un’ipersfera 3-dimensionale che, quasi incidentalmente, risulterà proprio il modello cosmologico offerto da Einstein nel 1917 per il suo universo chiuso e statico. Ed è proprio la curvatura che domina quella scena, oggetto matematico protagonista della teoria della relatività generale einsteniana. I personaggi prima elencati vengono comunque narrati anche nelle loro salienti vicende umane, a volte altamente drammatiche, come accadde per esempio per Riemann e Tullio Levi-Civita. In un certo senso, la storia della curvatura accompagna la storia dell’umanità.Benché inizialmente sia stato generato da un disegno didattico, il volume è indirizzato ad un pubblico non necessariamente studentesco, con una cultura scientifica di base.Table of Contents1 Tracce di cosmologia.- 2 Prima di Gauss.- 3 Gauss.- 4 Riemann.- 5 Christoffel.- 6 Ricci Curbastro.- 7 Levi-Civita.- 8 Tracce di geometria differenziale.- 9 Einstein.

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Book SynopsisIn the tradition of EuroComb'01 (Barcelona), Eurocomb'03 (Prague), EuroComb'05 (Berlin), Eurocomb'07 (Seville), Eurocomb'09 (Bordeaux), and Eurocomb'11 (Budapest), this volume covers recent advances in combinatorics and graph theory including applications in other areas of mathematics, computer science and engineering. Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.Table of Contents90 to 100 extended abstracts accepted by the Program Committee of Eurocomb 2013, formed by 24 experts in the field, for presentation at the forthcoming Conference Eurocomb 2013, Pisa, September 3-9, 2013.

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Book Synopsis​This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.Table of ContentsImre Bárány: Tensors, colours, octahedral.- Maria Chudnovsky: Cliques and stable sets in undirected graphs.- Mauro Di Nasso: A taste of nonstandard methods in combinatorics of numbers.- Béla Bollobás, Zoltán Füredi, Ida Kantor, G. O. H. Katona and Imre Leader: A coding problem for pairs of subsets.- Jirí Matousek: String graphs and separators.- Jaroslav Nesetril and Patrice Ossona de Mendez: On first-order definable colorings.- Ryan Schwartz and József Solymosi: Combinatorial applications of the subspace theorem.- Peter Hegarty and Dmitry Zhelezov: Can connected commuting graphs of finite groups have arbitrarily large diameter?

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Book SynopsisThis book contains select papers on mathematical analysis and modeling, discrete mathematics, fuzzy sets, and soft computing. All the papers were presented at the international conference on FIM28-SCMSPS20 virtually held at Sri Sivasubramaniya Nadar (SSN) College of Engineering, Chennai, India, and Stella Maris College (Autonomous), Chennai, from November 23–27, 2020. The conference was jointly held with the support of the Forum for Interdisciplinary Mathematics. Both the invited articles and submitted papers were broadly grouped under three heads: Part 1 on analysis and modeling (six chapters), Part 2 on discrete mathematics and applications (six chapters), and Part 3 on fuzzy sets and soft computing (three chapters).Table of ContentsPART I ANALYSIS AND MODELLINGThe Second- and Third-order Hermitian Toeplitz Determinants for Some Subclasses of Analytic Functions Associated with Exponential Function,P.Gurusamy, R. Jayasankar and S. SivasubramanianSome Results on a Starlike Class with Respect to $(j, m) $-symmetric FunctionsK. Renuka Devi, S. Sivasubramanian, Hamid Shamsan and S. LathaExperimental Evaluation of Four Intermediate Filters to Improve the Motion Field EstimationVanel Lazcano and Claudio Isa-MohorOn the $s^{th}$ Derivative of a PolynomialBarchand Chanam and Kshetrimayum KrishnadasOn the Problem of Pricing a Double Barrier Option in a Modified Black–Scholes Environment G. Venkiteswaran and S. UdayabaskaranCaputo Sequential Fractional Differential Equations with ApplicationsAghalaya S. Vatsala and Govinda PageniPART II DISCRETE MATHEMATICS AND APPLICATIONSHerscovici’s Conjecture on Product of Some Complete Bipartite GraphsA. Lourdusamy and S. Saratha NellainayakiOn Fault-Tolerant Metric Dimension of Heptagonal Circular Ladder and Its Related GraphsSunny Kumar Sharma and Vijay Kumar BhatBKS Fuzzy Inference Employing h-ImplicationsSayantan Mandal and Balasubramaniam Jayaram Note on Distributivity of Different String Operations over Language SetsUjjwal Kumar Mishra, Kalpana Mahalingam and Rama RaghavanA Generalization of Chi-binding FunctionsM. A. Shalu and T. P. SandhyaA Short Proof of Ore’s f-factor Theorem using FlowsSriraman Sridharan and Patrick VilamajoPART III FUZZY SETS AND SOFT COMPUTINGA Decision-making Problem Involving Soft Fuzzy Number Valued Information System: Energy Efficient Light Emitting Diode BlubsFelbin C. Kennedy, Masilla Moses Kennedy, Arul Roselet Meryline S. andJayachandiran M.Role of Single-valued Linear Octagonal Neutrosophic Numbers in Multi-attribute Decision-making ProblemsSubasri S., Arul Roselet Meryline S. and Felbin C. Kennedy

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Book SynopsisMathematical Logic.- Sets and Relations.- Functions.- Methods of Proofs.- Elementary Combinatorics.- Recurrences and Generating Functions.- Graph Theory.- Algebraic Systems.- Posets, Lattices and Boolean Algebras.- Automata Theory and Formal Languages.- Some Further Applications.

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Book SynopsisProfessor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for "his advancement of our understanding of the complexity of computation in a significant and profound way." This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook's synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook's ideas and their enduring impact on the research community. The book also contains biographical material, Cook's Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.

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Book SynopsisA CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, third edition continues to clearly show the usefulness of this subject for both students and researchers.The research in combinatorics of permutations has advanced rapidly since this book was published in a first edition. Now the third edition offers not only updated results, it remains the leading textbook for a course on the topic.Coverage is mostly enumerative, but there are algebraic, analytic, and topological parts as well, and applications.Since the publication of the second edition, there is tremendous progress in pattern avoidance (Chapters 4 and 5). There is also significant progress in the analytic combinatorics of permutations, which will be incorporated. A completely new technique from extremal comTable of ContentsForewardPreface to the First EditionPreface to the Second EditionPreface to the Third EditionAcknowledgementsIntroduction: No Way around It.1.In One Line and Close: Permutations as Linear Orders2.In One Line and Anywhere: Permutations as Linear Orders- Inversions3.In Many Circles: Permutations as Products of Cycles4.In Any Way but This: Pattern Avoidance—the Basics5.In This Way, but Nicely: Pattern Avoidance-Follow Up6.Mean and Insensitive: Random Permutations7.Permutations and the Rest: Algebraic Combinatorics of Permutations8.Get Them All: Algorithms and Permutations9.How Did We Get Here? Permutations as Genome RearrangementsDo Not Look Just Yet: Solutions to Odd-Numbered ExercisesReferencesList of Frequently Used NotationIndex

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThe interplay continues to grow between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences.Topics in Graph Theory is geared toward the more mathematically mature student. The first three chapters provide the basic definitions and theorems of graph theory and the remaining chapters introduce a variety of topics and directions for research. These topics draw on numerous areas of theoretical and applied mathematics, including combinatorics, probability, linear algebra, group theory, topology, operations research, and computer science. This makes the book appropriate for a first course at the graduate level or as a second course at the undergraduate level.The authors build upon material previously published in Graph Theory and Its Applications, Third Edition, by the same authors. That text covers material for both an underTable of Contents1. Foundations. 2. Isomorphisms and Symmetry. 3. Trees and Connectivity. 4. Planarity and Kuratowski’s Theorem. 5. Drawing Graphs and Maps. 6. Graph Colorings. 7. Measurement and Mappings. 8. Analytic Graph Theory. 9. Graph Colorings and Symmetry. 10. Algebraic Specification of Graphs. 11. Nonplanar Layouts.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis book has enjoyed considerable use and appreciation during its first four editions. With hundreds of students having learned out of early editions, the author continues to find ways to modernize and maintain a unique presentation.What sets the book apart is the excellent writing style, exposition, and unique and thorough sets of exercises. This edition offers a more instructive preface to assist instructors on developing the course they prefer. The prerequisites are more explicit and provide a roadmap for the course. Sample syllabi are included.As would be expected in a fifth edition, the overall content and structure of the book are sound.This new edition offers a more organized treatment of axiomatics. Throughout the book, there is a more careful and detailed treatment of the axioms of set theory. The rules of inference are more carefully elucidated.Additional new features include: An emphasis on the artTrade ReviewThe great strength of the book overall and of the chapters I read is a very accessible writing style, and extremely good exercises. The mix of discussion of advanced topics alongside the presentation of more elementary material is excellent. This is a product of having a highly accomplished and knowledgeable mathematician writing a textbook intended for not-so-advanced students.--David Walnut, George Washington UniversityTable of Contents1. Basic Logic 2. Methods of Proof 3. Set Theory 4. Relations and Functions 5. Group Theory 6. Number Systems 7. More on the Real Number System 8. A Glimpse of Topology 9. Elementary Number Theory 10. Zero-Knowledge Proofs and Cryptography 11. An Example of an Axiomatic Theory

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The Baseball Mysteries: Challenging Puzzles for Logical Detectives is a book of baseball puzzles, logical baseball puzzles. To jump in, all you need is logic and a casual fan's knowledge of the game. The puzzles are solved by reasoning from the rules of the game and a few facts.The logic in the puzzles is like legal reasoning. A solution must argue from evidence (the facts) and law (the rules). Unlike legal arguments, however, a solution must reach an unassailable conclusion.There are many puzzle books. But there's nothing remotely like this book. The puzzles here, while rigorously deductive, are firmly attached to actual events, to struggles that are reported in the papers every day.The puzzles offer a unique and scintillating connection between abstract logic and gritty reality.Actually, this book offers the reader an unlimited number of puzzles. Once you've solved a few of the challenges here, every boxscore you see in the pap

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Book SynopsisIn this book, various numerical methods are discussed in a comprehensive way. It delivers a mixture of theory, examples and MATLAB practicing exercises to help the students in improving their skills. To understand the MATLAB programming in a friendly style, the examples are solved. The MATLAB codes are mentioned in the end of each topic. Throughout the text, a balance between theory, examples and programming is maintained.Key Features Methods are explained with examples and codes System of equations has given full consideration Use of MATLAB is learnt for every method This book is suitable for graduate students in mathematics, computer science and engineering.Table of Contents1. Common Commands Used in Matlab. 2. System of Linear Equations. 3. Polynomial Interpolation. 4. Root Finding Methods. 5. Numerical Integration. 6. Solution of Initial Value Problems. 7. Boundary Value Problems.

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