论文标题
用于几个组合问题的实验数学方法
An Experimental Mathematics Approach to Several Combinatorial Problems
论文作者
论文摘要
实验数学是一种用于数学的实验方法，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。通过实验数学方法，本文涉及几个组合问题，并证明了实验数学的方法。我们从停车功能及其某些统计的时刻开始。然后，我们讨论跨越树木和“几乎对角线”矩阵，以说明实验数学的方法。我们还将实验数学应用于QuickSort算法以研究运行时间。最后，我们谈论有趣的和平皇后问题。
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.
