报告题目：Symmetric generating functions and permutation statistics
摘要：It is well known since the seminal work by Bousquet Mélou, Claesson, Dukes and Kitaev (2010) that certain refinements of the ascent sequences with respect to several natural statistics are in bijection with corresponding refinements of (2+2)-free posets and permutations that avoid a bi-vincular pattern. Different multiply-refined enumerations of ascent sequences and other bijectively equivalent structures have subsequently been extensively studied by various authors.
In this talk, I will present our recent results along this research line. Our main contributions are a bijective proof of a bi-symmetric septuple equidistribution of Euler—Stirling statistics on ascent sequences and a new transformation formula for non-terminating basic hypergeometric series expanded as an analytic function in base q around q=1, which is utilized to prove two (bi)-symmetric quadruple equidistrbutions on ascent sequences.
A by-product of our findings includes the affirmation of a conjecture (2018) about the bi-symmetric equidistribution between the quadruples of Euler—Stirling statistics on ascent sequences, that was motivated by a double Eulerian equidistribution due to Foot (1977).
报告人简介： 靳宇，厦门大学数学科学学院教授，国家高层次青年人才。西南大学本科，南开大学博士。在德国凯泽斯劳滕大学，奥地利维也纳科技大学和维也纳大学从事博士后研究。主要从事解析组合和离散概率方向的研究工作，已经在J. Combin. Theory Ser. A和Random Struct. Algor. 等重要学术期刊发表多篇文章。先后获得过美国生物数学协会Lee Segel奖学金，德国洪堡博士后奖学金，主持过德国国家基金委DFG的个人项目，奥地利国家基金委Elise-Richter项目。