报告题目：Enumeration of signed permutations by the parity of descent position

报告人：曾江 特级教授（University Lyon 1, France）

报告时间：2022 年 9 月 1 日（星期四） 15:00-16:00

报告地点：腾讯会议 ID：127 404 286

校内联系人：王毅 教授  联系电话：84708351-8099

报告摘要:  We show that Carlitz-Scoville's four-variable formula enumerating descents and rises of permutations by position has two special equivalent variants, which correspond, respectively, to H. Sun's bivariate refinement of the descent polynomials (Eulerian polynomials) and a refinement of Chebikin's alternating descent polynomials. After giving an alternative proof (without solving PDE) of Carlitz and Scoville's formula for permutations (type A), we prove a type-B analogue of Carlitz-Scoville's formula for signed permutations. Moreover, starting from the generating functions we derive an alternative proof of H. Sun and Sun-Zhai's gamma decomposition of bivariate Eulerian polynomials as well as a refinement of Petersen's gamma-positivity of the Eulerian polynomials of type B. This is a joint work with Qiongqiong Pan (Wenzhou University).

报告人简介：曾江，博士毕业于法国斯特拉斯堡大学（University Strasbourg）。现为法国里昂大学特级教授，曾就职于普林斯顿高等研究院及斯特拉斯堡大学，2015年荣获韩国数学科学研究院（NIMS）杰出学者 (Distinguished Scholar)。在Proc. London Math. Soc., Trans. Amer. Math. Soc., J. Combin. Theory Ser. A 等SCI期刊上发表了130多篇学术论文。他的主要工作在以下几方面：正交多项式及其矩和线性化系数的组合性质；对称函数的组合性质，分拆和q-级数；Coxeter群和词上的Euler-MacMahon统计量；经典序列、特殊函数的组合性质以及它们的q-模拟；组合序列的伽马正定性，组合矩阵的全正性。