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arXiv · 2201.11763

Quasisymmetric functions distinguishing trees

Jean-Christophe Aval·Karimatou Djenabou·Peter R. W. McNamara
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Abstract

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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Jean-Christophe Aval, Karimatou Djenabou, Peter R. W. McNamara. 2023-05-16. Quasisymmetric functions distinguishing trees. https://doi.org/10.5802/alco.273

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