Strong and powerful P-tableaux are conjectured to give lower and upper bounds for e-coefficients of chromatic symmetric functions, with exact interpretations proven for several families.
A signed $e$-expansion of the chromatic quasisymmetric function
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove a new signed elementary symmetric function expansion of the chromatic quasisymmetric function of any natural unit interval graph. We then use a sign-reversing involution to prove a new combinatorial formula for K-chains, which are graphs formed by joining cliques at single vertices. This formula immediately implies $e$-positivity and $e$-unimodality for K-chains. We also prove a version of our signed $e$-expansion for arbitrary graphs.
citation-role summary
method 1
citation-polarity summary
fields
math.CO 1years
2025 1verdicts
CONDITIONAL 1roles
method 1polarities
use method 1representative citing papers
citing papers explorer
-
Toward Lower Bounds for Chromatic Symmetric Functions in the Elementary Basis
Strong and powerful P-tableaux are conjectured to give lower and upper bounds for e-coefficients of chromatic symmetric functions, with exact interpretations proven for several families.