关于有禁排列计数问题的研究

Research on Enumeration Problem of Pattern-avoiding Permutations

有禁排列的相关计数问题是计数组合学的研究热点之一,在物理、化学、计算机科学中有着众多应用.本文主要对n元对称群S_(n),交错排列、Dumont排列、Ballot排列以及逆序列上有禁排列计数问题的相关结论进行总结,并介绍关于S_(n)上避免相邻模式以及带杠模式排列的相关研究成果.

The problem of relevant enumeration with pattern-avoiding permutations is one of the hot topics in enumeration combinatorics and has wide applications in physics,chemistry,and computer science.This paper summarizes the relevant result of the enumeration of pattern-avoiding permutations n-element symmetric group S_(n),alternating permutations,Dumont permutations,Ballot permutations,and inversion sequences.It also introduces relevant research results on avoiding vincular pattern and barred pattern in S_(n).