报告题目：The $e$-positivity of the chromatic symmetric functions and the inverse Kostka matrix
报告人：王诗韵 博士
邀请人：张 毅 博士
报告时间：2024年3月28日（周四）09:00-10:30
腾讯会议：腾讯会议：249-958-027
报告摘要：The Stanley-Stembridge conjecture states that each chromatic symmetric function is positive in the basis of elementary symmetric functions. Shareshian-Wachs established a q-version of this conjecture on chromatic quasisymmetric functions. We expand the chromatic quasisymmetric functions for Dyck paths of bounce number three in the elementary symmetric function basis using a combinatorial interpretation of the inverse of the Kostka matrix studied in E\~{g}ecio\~{g}lu-Remmel (1990). We prove that certain coefficients in this expansion are positive. We establish the $e$-positivity of an extended class of chromatic quasisymmetric functions for Dyck paths of bounce number three beyond the hook-shape case of Cho-Huh (2019).
报告人简介：Shiyun Wang's educational background includes a B.A. in management from Central South University in China, a Master of Public Administration from the University of Southern California (USC), and an M.S. in Mathematics from California State University Long Beach (CSULB). She obtained her Ph.D. degree in mathematics from USC in 2023. Currently, She works as a Postdoctoral Associate at the University of Minnesota Twin Cities. Shiyun has developed research interests in algebraic and enumerative combinatorics, tableaux combinatorics, symmetric functions, and quasi-symmetric functions in relation to representation theory. Her current work focuses on the Stanley-Stembridge Conjecture and row-strict dual immaculate functions with connections to 0-Hecke algebra.
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数学与统计学院
江苏省应用数学（南京信息工程大学）中心
江苏省系统建模与数据分析国际合作联合实验室
2024年3月27日