Statistics of partial permutations via Catalan matrices
學年 111
學期 2
出版(發表)日期 2023-02-01
作品名稱 Statistics of partial permutations via Catalan matrices
著者 Yen-Jen Cheng; Sen-Peng Eu; Hsiang-Chun Hsu
著錄名稱、卷期、頁數 Advances in Applied Mathematics 143, 102451
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.
關鍵字 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
語言 en_US
ISSN 0196-8858;1090-2074
期刊性質 國外
收錄於 SCI
國別 USA
出版型式 ,電子版,紙本