报告人：Jiang Zeng(法国里昂一大)

时间：2021年6月29日15:00开始

腾讯会议ID:436 707 762

摘要:There is a close relationship between continued fractions, Hankel determinants, and orthogonal polynomials. Many of the most important sequences in enumerative combinatorics arise as moments of well-known orthogonal polynomials. One characteristic of these sequences is that their ordinary generating functions have simple continued fractions.

       In the first talk, starting from the moment sequences of classical orthogonal polynomials we derive the orthogonality purely algebraically. We consider also the moments of (q=1) classical orthogonal polynomials, and study those cases in which the exponential generating function has a nice form and show that the generalized Dumont-Foata polynomials, which refine  both Genocchi numbers and median Genocchi numbers,  are the moments of rescaled continuous dual Hahn polynomials.

       Recently,  as a refinement of the median Genocchi numbers, Eu-Fu-Lai-Lo studied  the descent polynomials of even-odd descent permutations and proved that they are  gamma-positive. In the second talk, using combinatorial theory of continued fractions and bijections we define a natural (p,q)-analogue of their polynomials and show that these polynomials provide  a  nice (p,q)-analogue of the J-fraction and gamma-positivity.

简介:Jiang Zeng为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，其主要研究方向为组合学、特殊函数及数论。曾教授已在JCTA、Adv. Appl. Math.、Trans. Amer. Math. Soc.、European J. Combin.、Discrete Math.、Ramanujan J.等权威期刊发表学术论文130多篇，现任杂志Séminaire Lotharingien de Combinatoire编委，Journal of Combinatorics and Number Theory主编，华东师范大学海外高层次专家等。

邀请人：傅士硕

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