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The $e$-positivity of the chromatic symmetric functions and the inverse Kostka matrix
- Publication Year :
- 2022
-
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 E\u{g}ecio\u{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 symmetric functions for Dyck paths of bounce number three beyond the "hook-shape" case of Cho-Huh (2019).<br />Comment: 24 pages
- Subjects :
- Mathematics - Combinatorics
05A05, 05E05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2210.07567
- Document Type :
- Working Paper