Séminaire Lotharingien de Combinatoire, 91B.106 (2024), 12 pp.
Eric Marberg
Kromatic Quasisymmetric Functions
Abstract.
We provide a construction for the kromatic symmetric function
X-G of a graph introduced by Crew, Pechenik, and Spirkl using combinatorial (linearly compact) Hopf algebras. As an application, we show that
X-G has a positive expansion into multifundamental quasisymmetric functions. We also study two related quasisymmetric q-analogues of
X-G, which are K-theoretic generalizations of the quasisymmetric chromatic function of Shareshian and Wachs. We classify exactly when one of these analogues is symmetric. For the other, we derive a positive expansion into symmetric Grothendieck functions for graphs G that are natural unit interval orders.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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