报告题目： A weight-dependent inversion statistic and Catalan numbers.
报 告 人：傅士硕 重庆大学“百人计划”特聘研究员
摘要：We introduce a weight-dependent extension of the classical Mahonian statistic on permutations, the inversion number. This immediately gives us a new weight-dependent extension of $n!$. When we restrict to $312$-avoiding permutations, our extension gives rise to a weight-dependent family of Catalan numbers. We investigate basic properties of these numbers that highly resemble those of the classical case, such as their recurrence relation, Hankel determinants, as well as continue fraction expansion. Specializations of these weight-dependent Catalan numbers present interesting links with well-known combinatorial objects, such as perfect matchings and Euler numbers. We will also develop certain bi-weighted Catalan numbers that generalize Garsia and Haiman's $q,t$-Catalan numbers and again satisfy interesting properties. This talk is based on joint work with Michael Schlosser.
个人概况：傅士硕，博士毕业于宾夕法尼亚州州立大学，现任职重庆大学“百人计划”特聘研究员。研究兴趣主要为组合数学中的整数分拆理论、排列统计量同分布问题以及组合序列的伽马非负性。已在J. Combin. Theory Ser. A, Adv. Appl. Math., Rama J., J. Number Theory等杂志发表论文20余篇，主持过国家自然科学基金青年基金一项。