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arXiv · 2006.00657

Chromatic symmetric functions from the modular law

Alex Abreu·Antonio Nigro
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Abstract

In this article we show how to compute the chromatic quasisymmetric function of indifference graphs from the modular law introduced by Guay-Paquet. We provide an algorithm which works for any function that satisfies this law, such as unicellular LLT polynomials. When the indifference graph has bipartite complement it reduces to a planar network, in this case, we prove that the coefficients of the chromatic quasisymmetric function in the elementary basis are positive unimodal polynomials and characterize them as certain $q$-hit numbers (up to a factor). Finally, we discuss the logarithmic concavity of the coefficients of the chromatic quasisymmetric function.

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Alex Abreu, Antonio Nigro. 2020-06-01. Chromatic symmetric functions from the modular law. https://arxiv.org/abs/2006.00657

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