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Article Dans Une Revue Algebraic Combinatorics Année : 2022

Quasisymmetric functions distinguishing trees

Résumé

A famous conjecture of Stanley states that his chromatic symmetric function distinguishes trees. As a quasisymmetric analogue, we conjecture that the chromatic quasisymmetric function of Shareshian and Wachs and of Ellzey distinguishes directed trees. This latter conjecture would be implied by an affirmative answer to a question of Hasebe and Tsujie about the $P$-partition enumerator distinguishing posets whose Hasse diagrams are trees. They proved the case of rooted trees and our results include a generalization of their result.
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hal-03796697 , version 1 (06-10-2022)

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Jean-Christophe Aval, Karimatou Djenabou, Peter R. W. Mcnamara. Quasisymmetric functions distinguishing trees. Algebraic Combinatorics, In press. ⟨hal-03796697⟩

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