Séminaire Lotharingien de Combinatoire, 93B.153 (2025), 12 pp.

Jim Haglund, Jaeseong Oh and Meesue Yoo

α-Chromatic Symmetric Functions

Abstract. In this extended abstract, we introduce the \emph{α-chromatic symmetric functions} χ_π^(α)[X;q], extending Shareshian and Wachs' chromatic symmetric functions with an additional real parameter α. We present positive combinatorial formulas with explicit interpretations. Notably, we show an explicit monomial expansion in terms of the α-binomial basis and an expansion into certain chromatic symmetric functions in terms of the α-falling factorial basis. We also exhibit various Schur positivity results.

Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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