A graph's chromatic quasisymmetric function is symmetric only under strong constraints; the paper proves connected DAGs with multiple sources/sinks are nonsymmetric and identifies a new symmetric family.
The $e$-positivity of the chromatic symmetric functions and the inverse Kostka matrix
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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).
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
When is the chromatic quasisymmetric function symmetric?
A graph's chromatic quasisymmetric function is symmetric only under strong constraints; the paper proves connected DAGs with multiple sources/sinks are nonsymmetric and identifies a new symmetric family.