Description
Book SynopsisEnumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years'' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the RedfieldPólya theory of cycle indices, Möbius inversion, the Tutte polynomial, and species.
Trade Review'It's indeed a very good introduction to enumerative combinatorics and has all the trappings of a pedagogically sound enterprise, in the old-fashioned sense: exercises, good explanations (not too terse, but certainly not too wordy), and mathematically serious (nothing namby-pamby here). It's an excellent book.' Michael Berg, MAA Reviews
'Cameron's Notes on Counting is a clever introductory book on enumerative combinatorics … Overall, the text is well-written with a friendly tone and an aesthetic organization, and each chapter contains an ample number of quality exercises. Summing Up: Recommended.' A. Misseldine, CHOICE
Table of Contents1. Introduction; 2. Formal power series; 3. Subsets, partitions and permutations; 4. Recurrence relations; 5. The permanent; 6. q-analogues; 7. Group actions and cycle index; 8. Mobius inversion; 9. The Tutte polynomial; 10. Species; 11. Analytic methods: a first look; 12. Further topics; 13. Bibliography and further directions; Index.
