几个组合问题的实验数学方法

Yukun Yao
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引用次数: 0

摘要

实验数学是数学的一种实验方法,其中使用编程和符号计算来研究数学对象,识别属性和模式,发现事实和公式,甚至自动证明定理。本文运用实验数学的方法,研究了几种组合问题,并对实验数学的方法进行了阐述。我们从停车函数和某些统计量的矩开始。然后我们讨论了生成树和“几乎对角”矩阵来说明实验数学的方法。我们还将实验数学应用到快速排序算法中来研究其运行时间。最后我们来谈谈有趣的和平女王问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An experimental mathematics approach to several combinatorial problems
Experimental mathematics is an experimental approach to mathematics in which programming and symbolic computation are used to investigate mathematical objects, identify properties and patterns, discover facts and formulas and even automatically prove theorems. With an experimental mathematics approach, this dissertation deals with several combinatorial problems and demonstrates the methodology of experimental mathematics. We start with parking functions and their moments of certain statistics. Then we discuss about spanning trees and "almost diagonal" matrices to illustrate the methodology of experimental mathematics. We also apply experimental mathematics to Quicksort algorithms to study the running time. Finally we talk about the interesting peaceable queens problem.
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