报 告 人: 曾江 教授

报告题目:Euler numbers and André Permutations





sb沙巴体育官方投注   曾江,法国里昂第一大学教授,博士生导师,师从于组合数学国际权威 Dominique Foata教授。他曾是美国普林斯顿高等研究院的访问学者。主要研究组合数学、特殊函数、数论,在Journal of Combinaotrial Theory Series A, Advances in Applied Mathematics,Transactions of the American Mathematical Society,Proceedings of the London Mathematical Society,SIAM Journal on Discrete Mathematics,SIAM Journalon Mathematical Analysis,Journal of Number Theory等权威期刊发表学术论文100多篇,现任杂志 Seminaire Lotharingien de Combinatoire编委,Journal of Combinatorics and Number Theory的主编


   The Euler numbers are the coeffcients in the Taylor expansion of tan x+sec x. A classical result of Andre says that these coeffcients enumerate alternating permutations. In the 1970's Foata and Shcutzenberger found another family of permutations, called Andre permutations, also enumerated by Euler numbers and proved that the descent polynomials of Andre permutations are related to the gamma-coeffcients of Eulerian polynomials. In this talk, I will present a (p; q)-analogue of their result using the combinatorial theory of continued fractions, which gives a satisfactory answer to a conjecture of Branden on the gamma-coeffcients of his (p; q)-analogue of Eulerian polynomials. In particular, this answers a recent question of G.N. Hanon his q-Euler numbers