| 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 |
| 作品名稱（其他語言） | |
| 著者 | Yen-Jen Cheng; Sen-Peng Eu; Hsiang-Chun Hsu |
| 單位 | |
| 出版者 | |
| 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 |
| 產學合作 | |
| 通訊作者 | |
| 審稿制度 | 是 |
| 國別 | USA |
| 公開徵稿 | |
| 出版型式 | ,電子版,紙本 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/122895 ) |
| SDGS | 優質教育 |
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