Séminaire Lotharingien de Combinatoire, 89B.25 (2023), 12 pp.
Byung-Hak Hwang
Chromatic Quasisymmetric Functions and Noncommutative P-symmetric Functions
Abstract.
For a natural unit interval order P, we introduce a combinatorial
operation, called a \emph{local flip}, on proper colorings of P.
This operation defines an equivalence relation on the proper
colorings, and the equivalent relation refines the ascent statistic introduced
by Shareshian and Wachs.
We also define analogues of noncommutative symmetric functions.
They reflect properties of P and local flips,
and lead us to positive expansions of the
chromatic quasisymmetric functions into several symmetric function bases.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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