Random sequential packing of cubes into torus

引入了非常简化的模型来从数学上理解随机顺序包装模型。一维模型有时被称为停车问题。为了得到一维的堆积密度、最小间隙的分布等，必须研究经典分析。一般多维随机序贯立方体（超立方体）的填充密度是一个众所周知的未解问题。实验分析通常用于解决这个问题。在保留原通用模型特征的基础上，引入了简化的立方体和环面多维模型，并引入了组合建模的组合分析。本文在不使用计算机模拟的情况下，成功地从数学上获得了角偏好随机顺序立方体填充成更大立方体的期望立方体数，这将有助于解决立方体随机顺序填充成环面的问题。

Very simplified models are introduced to understand the random sequential packing models mathematically. The 1-dimensional model is sometimes called the Parking Problem. 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. We introduced simplified multi-dimensional models of cubes and torus, which keep the character of the original general model, and introduced a combinatorial analysis for combinatorial modelings. Here we succeeded in obtaining expected number of cube for a corner preference random sequential packing of cubes into a larger cube mathmeatically without using computer simulations, which will help to solve our original problemrandom sequential packing of cubes into torus.