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標題:Signed countings of types B and D permutations and t,q-Euler numbers
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
語言英文(美國)
ISSN0196-8858;1090-2074
期刊性質國外
收錄於SCI;
產學合作
通訊作者
審稿制度
國別美國
公開徵稿
出版型式,電子版,紙本
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