Description
Book SynopsisIn this volume very simplified models are introduced to understand the random sequential packing models mathematically. The 1-dimensional model is sometimes called the Parking Problem, which is known by the pioneering works by Flory (1939), Renyi (1958), Dvoretzky and Robbins (1962). To obtain a 1-dimensional packing density, distribution of the minimum of gaps, etc., the classical analysis has to be studied. The packing density of the general multi-dimensional random sequential packing of cubes (hypercubes) makes a well-known unsolved problem. The experimental analysis is usually applied to the problem. This book introduces simplified multi-dimensional models of cubes and torus, which keep the character of the original general model, and introduces a combinatorial analysis for combinatorial modelings.
Table of ContentsRandom Interval Packing; The Speed of Convergence to the Renyi Constant; The Dvoretzky Robbins Central Limit Theorem; Gap Size; The Minimum of Gaps; Kakutani's Interval Splitting; Sequential Bisection and Binary Search Tree; Car Parking with Spin; Golay Code and Random Packing; Discrete Cube Packing; Torus Cube Packing; Continuous Random Cube Packing in Cube and Torus; Combinatorial Enumeration.
