The e-positivity of the chromatic symmetric functions and the inverse Kostka matrix

2022/10/14 by Wang, Shiyun
#05A05 #05E05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.07567

Abstract

We expand the chromatic symmetric 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 Eğecioğlu-Remmel (1990). We prove that certain coefficients in this expansion are positive. We establish the e-positivity of an extended class of chromatic symmetric functions for Dyck paths of bounce number three beyond the "hook-shape" case of Cho-Huh (2019).

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