Statistics of partial permutations via Catalan matrices

Yen Jen Cheng*, Sen Peng Eu, Hsiang Chun Hsu


研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)


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 s=2ℓ+1 and t=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.

期刊Advances in Applied Mathematics
出版狀態已發佈 - 2023 2月

ASJC Scopus subject areas

  • 應用數學


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