Signed countings of types B and D permutations and t,q-Euler numbers

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题名:	Signed countings of types B and D permutations and t,q-Euler numbers
作者:	Eu, Sen-Peng;Fu, Tung-Shan;Hsu, Hsiang-Chun;Liao, Hsin-Chieh
关键词:	Euler number;Springer number;Signed permutations;Derangements;Continued fractions;Weighted bicolored Motzkin paths
日期:	2018-06
上传时间:	2020-02-11 12:10:18 (UTC+8)
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.
關聯:	Advances in Applied Mathematics 97, p.1-26
DOI:	10.1016/j.aam.2018.02.004
显示于类别:	[數學學系暨研究所] 期刊論文

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