期刊論文
| 學年 | 106 |
|---|---|
| 學期 | 2 |
| 出版（發表）日期 | 2018-06-30 |
| 作品名稱 | Signed countings of types B and D permutations and t,q-Euler numbers |
| 作品名稱（其他語言） | |
| 著者 | Sen-Peng Eu; Tung-Shan Fu; Hsiang-Chun Hsu; Hsin-Chieh Liao |
| 單位 | |
| 出版者 | |
| 著錄名稱、卷期、頁數 | Advances in Applied Mathematics 97, p.1-26 |
| 摘要 | It is a classical result that the parity-balance of the number of weak excedances of all permutations (derangements, respectively) of length n is the Euler number , alternating in sign, if n is odd (even, respectively). Josuat-Vergès obtained a q-analog of the results respecting the number of crossings of a permutation. One of the goals in this paper is to extend the results to the permutations (derangements, respectively) of types B and D, on the basis of the joint distribution in statistics excedances, crossings and the number of negative entries obtained by Corteel, Josuat-Vergès and Kim. Springer numbers are analogous Euler numbers that count the alternating permutations of type B, called snakes. Josuat-Vergès derived bivariate polynomials and as generalized Euler numbers via successive q-derivatives and multiplications by t on polynomials in t. The other goal in this paper is to give a combinatorial interpretation of and as the enumerators of the snakes with restrictions. |
| 關鍵字 | Euler number;Springer number;Signed permutations;Derangements;Continued fractions;Weighted bicolored Motzkin paths |
| 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/987654321/118059 ) |