Quasisymmetric functions distinguishing trees
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913599653412864 |
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| author | Aval, Jean-Christophe Djenabou, Karimatou McNamara, Peter R. W. |
| author_facet | Aval, Jean-Christophe Djenabou, Karimatou McNamara, Peter R. W. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_11763 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quasisymmetric functions distinguishing trees Aval, Jean-Christophe Djenabou, Karimatou McNamara, Peter R. W. Combinatorics 05E05 (Primary), 06A07, 06A11, 05C05, 05C20 (Secondary) 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. |
| title | Quasisymmetric functions distinguishing trees |
| topic | Combinatorics 05E05 (Primary), 06A07, 06A11, 05C05, 05C20 (Secondary) |
| url | https://arxiv.org/abs/2201.11763 |