大连理工大学数学科学学院
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【University Lyon 1, France】Enumeration of signed permutations by the parity of descent position

2022年08月29日 15:01  点击:[]

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 9 1 日(星期四) 15:00-16:00

报告地点:腾讯会议 ID127 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 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。


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