Geodesic
Characters and chromatic symmetric functions
Mark Skandera1
1Lehigh University
The electronic journal of combinatorics, Tome 28 (2021) no. 2
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Let $P$ be a poset, $\mathrm{inc}(P)$ its incomparability graph, and $X_{\mathrm{inc}(P)}$ the corresponding chromatic symmetric function, as defined by Stanley in Adv. Math., 111 (1995) pp.166–194. Let $\omega$ be the standard involution on symmetric functions. We express coefficients of $X_{\mathrm{inc}(P)}$ and $\omega X_{\mathrm{inc}(P)}$ as character evaluations to obtain simple combinatorial interpretations of the power sum and monomial expansions of $\omega X_{\mathrm{inc}(P)}$ which hold for all posets $P$. Consequences include new combinatorial interpretations of the permanent, induced trivial character immanants, and power sum immanants of totally nonnegative matrices, and of the sum of elementary coefficients in the Shareshian-Wachs chromatic quasisymmetric function $X_{\mathrm{inc}(P),q}$ when $P$ is a unit interval order.
DOI : 10.37236/9726
Classification : 05E05, 05C15, 15A15, 20C08, 06A07
Mots-clés : Shareshian-Wachs chromatic quasisymmetric function

Mark Skandera  1

1 Lehigh University 
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Mark Skandera. Characters and chromatic symmetric functions. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/9726

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