Geodesic
Quasisymmetric functions distinguishing trees
Aval, Jean-Christophe1 ; Djenabou, Karimatou2 ; McNamara, Peter R. W.3
1 LaBRI, CNRS, Université de Bordeaux 351 cours de la Libération 33405 Talence France
2 African Institute for Mathematical Sciences 6 Melrose Road Muizenberg 7945 South Africa
3 Department of Mathematics, Bucknell University Lewisburg, PA 17837 USA
Algebraic Combinatorics, Tome 6 (2023) no. 3, pp. 595-614

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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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DOI : 10.5802/alco.273
Classification : 05E05, 06A07, 06A11, 05C05, 05C20
Keywords: chromatic, quasisymmetric function, digraph, poset, P-partition, rooted tree

Aval, Jean-Christophe 1 ; Djenabou, Karimatou 2 ; McNamara, Peter R. W. 3

1 LaBRI, CNRS, Université de Bordeaux 351 cours de la Libération 33405 Talence France
2 African Institute for Mathematical Sciences 6 Melrose Road Muizenberg 7945 South Africa
3 Department of Mathematics, Bucknell University Lewisburg, PA 17837 USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Aval, Jean-Christophe; Djenabou, Karimatou; McNamara, Peter R. W. Quasisymmetric functions distinguishing trees. Algebraic Combinatorics, Tome 6 (2023) no. 3, pp. 595-614. doi: 10.5802/alco.273

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