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The Chromatic Quasisymmetric Class Function of a Digraph

Abstract

We introduce a quasisymmetric class function associated with a group acting on a double poset or on a directed graph. The latter is a generalization of the chromatic quasisymmetric function of a digraph introduced by Ellzey, while the former is a generalization of a quasisymmetric function introduced by Grinberg. We prove representation-theoretic analogues of classical and recent results, including F-positivity, and combinatorial reciprocity theorems. We deduce results for orbital quasisymmetric functions, and study a generalization of the notion of strongly flawless sequences.

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Correspondence to Jacob A. White.

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Communicated by Vasu Tewari.

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White, J.A. The Chromatic Quasisymmetric Class Function of a Digraph. Ann. Comb. (2021). https://doi.org/10.1007/s00026-021-00556-1

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Keywords

  • Chromatic polynomials
  • Quasisymmetric functions
  • Poset partitions
  • Group actions

Mathematics Subject Classification

  • 05E05
  • 05E18