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A signed $e$-expansion of the chromatic quasisymmetric function
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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.
Forward citations
Cited by 2 Pith papers
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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.
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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.
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