Random Sequential Packing of CubesIn 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.
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Contents
| 1 | |
2 The Flory model | 9 |
3 Random interval packing | 23 |
4 On the minimum of gaps generated by 1dimensional random packing | 39 |
5 Integral equation method for the 1dimensional random packing | 69 |
6 Random sequential bisection and its associated binary tree | 83 |
7 The unified Kakutani Renyi model | 99 |
8 Parking cars with spin but no length | 123 |