Random sequential packing of cubes
著者
書誌事項
Random sequential packing of cubes
World Scientific, c2011
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- Random 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.
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