Pattern avoidance of generalized permutations
Pattern avoidance of generalized permutations
复制标题
DOI：
10.1016/j.aam.2019.01.007
复制
发表时间：
2018-04
期刊：
影响因子：
--
通讯作者：
Zhousheng Mei;Suijie Wang
中科院分区：
文献类型：
--
作者：
Zhousheng Mei;Suijie Wang
本文研究了广义置换的模式回避问题，证明了所有避免π的广义置换的个数与π∈s3的选择无关，从而推广了关于避免π∈s3的置换的经典结果。在对Dyck路径和Riordan路径进行扩展的基础上，引入了Catalan - Riordan路径，该路径是加泰罗尼亚数差分数组的组合解释。作为应用，我们用两种方法解释Motzkin数和Riordan数，通过两行的半标准Young表和避免π∈s3的广义置换。与Lewis的方法类似，我们建立了从广义排列到矩形半标准杨表的双射，这将恢复文献中已知的几个结果。
In this paper, we study pattern avoidances of generalized permutations and show that the number of all generalized permutations avoiding π is independent of the choice of π∈ S 3, which extends the classic results on permutations avoiding π∈ S 3. Extending both Dyck path and Riordan path, we introduce the Catalan–Riordan path which turns out to be a combinatorial interpretation of the difference array of Catalan numbers. As applications, we interpret both Motzkin and Riordan numbers in two ways, via semistandard Young tableaux of two rows and generalized permutations avoiding π∈ S 3. Analogous to Lewis's method, we establish a bijection from generalized permutations to rectangular semistandard Young tableaux which will recover several known results in the literature.