A composition calculus method for graph positivity problems
数学专题报告
报告题目(Title)：A composition calculus method for graph positivity problems
报告人(Speaker)：王国亮教授 （北京理工大学）
地点(Place)：后主楼1124
时间(Time)：2024 年 1 月 4 日（周四） 15:00--16:00
邀请人(Inviter)：徐敏
报告摘要
This talk is a recent progress on the e-positivity of graphs. Inspired by Shareshianand Wachs’s exquisite formula for the chromatic symmetric function of paths, we develop a composition calculus method to produce neat formulas for chromatic symmetricfunctions in terms of symmetric functions indexed by compositions. In particular, weobtain short and sweet Λ-positive noncommutative analogs for the chromatic symmetric functions of cycles, tadpoles and some K-chains such like barbells, lollipops, lariates, and generalized bulls. As an application of the composition calculus, we establish thee-positivity of double-tail tadpoles, which is obtained by attaching a second tail to atadpole so that the two degree 3 vertices are adjacent.
主讲人简介
王国亮，北京理工大学数学教授，研究方向是代数组合学。于 2010 年获南开大学博士学位，曾在北京国际数学研究中心（BICMR）和以色列海法大学做博士后工作，访问美国麻省理工学院（MIT）和法国 Gaspard-Monge 信息实验室（LIGM），近期研究兴趣是图的色对称函数的正性分类问题，即确定图的色对称函数是否具有e-正性或 Schur 正性。曾主持三项国家自然科学基金，现任中国运筹学会图论组合分会理事。
