离散对象的计数

The enumeration of discrete objects

本文从集合概念出发,分别就重集,全序和偏序集,计数基本原理等内容,汇总了线状和环状的排列与组合,整数分析对应的标准和半标准杨表计数的常用计数解题的方法和技巧.随后从生成函数,格路计数和Polya计数定理等方面,用实例的方法说明它们在离散对象计数方面的应用.最后,通过求解化学中同分异构体计数问题的简短编程,介绍了计算机辅助软件Maple在快速高效求解离散对象计数问题方面的作用.

From the concept of set,we summarize the methods and skills of the enumeration of discrete objects in terms of multiset,totally ordered set,and partial ordered set,a fundamental principle of a count,etc.Then the application of generating function,enumeration of lattice paths,and Polya′s enumeration theorem in discrete object counting is illustrated by examples.Finally,the power of Maple,a computer-aided software,in solving discrete object counting problems quickly and efficiently is introduced through a brief program of solving isomers in chemistry.