Statistics of partial permutations via Catalan matrices

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题名:	Statistics of partial permutations via Catalan matrices
作者:	Cheng, Yen-Jen;Eu, Sen-Peng;Hsu, Hsiang-Chun
关键词:	Permutation;Partial permutation;Catalan matrix;Statistic;Set-valued statistic;Fixed point;Inversion;Descent;Cycle;Excedance;Right-to-left minimum;Connected permutation;Cycle-up-down permutation
日期:	2023-02
上传时间:	2023-04-28 16:23:16 (UTC+8)
出版者:	Academic Press
摘要:	A generalized Catalan matrix (an,k)n,k≥0 is generated by two seed sequences s=(s0,s1,…) and t=(t1,t2,…) together with a recurrence relation. By taking sℓ=2ℓ+1 and tℓ=ℓ2 we can interpret an,k as the number of partial permutations, which are n×n 0,1-matrices of k zero rows with at most one 1 in each row or column. In this paper we prove that most of fundamental statistics and some set-valued statistics on permutations can also be defined on partial permutations and be encoded in the seed sequences. Results on two interesting permutation families, namely the connected permutations and cycle-up-down permutations, are also given.
關聯:	Advances in Applied Mathematics 143, 102451
DOI:	10.1016/j.aam.2022.102451
显示于类别:	[應用數學與數據科學學系] 期刊論文

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