Random Sequential Packing of Cubes

This is the proceedings of the ICM2002 Satellite Conference on Algebras. Over 175 participants attended the meeting. The opening ceremony included an address by R. Gonchidorsh, former vice-president of the Mongolian Republic in Uaalannbaatar. The topics covered at the conference included general algebras, semigroups, groups, rings, hopf algebras, modules, codes, languages, automation theory, graphs, fuzz algebras and applications In 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 ... Read more... Preface; Contents; 1. Introduction; 2. The Flory model; 3. Random interval packing; 4. On the minimum of gaps generated by 1-dimensional random packing; 5. Integral equation method for the 1-dimensional random packing; 6. Random sequential bisection and its associated binary tree; 7. The unified Kakutani Renyi model; 8. Parking cars with spin but no length; 9. Random sequential packing simulations; 10. Discrete cube packings in the cube; 11. Discrete cube packings in the torus; 12. Continuous random cube packings in cube and torus; Appendix A Combinatorial Enumeration; Bibliography; Index In 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. Book jacket