Proof of a conjecture on graph polytope
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913019873722368 |
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| author | Liu, Feihu |
| author_facet | Liu, Feihu |
| contents | Graph polytopes arising from vertex-weighted graphs were first introduced by Bóna, Ju, and Yoshida. We prove a conjecture stating that for any simple connected graph, the numerator polynomial of the Ehrhart series of its graph polytope is palindromic, using Stanley's reciprocity theorem. Furthermore, we introduce hypergraph polytopes and establish that every simple, connected, unimodular hypergraph polytope is an integer polytope. Additionally, for simple connected uniform hypergraph polytopes, we demonstrate that the numerator polynomial of their Ehrhart series is palindromic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proof of a conjecture on graph polytope Liu, Feihu Combinatorics Graph polytopes arising from vertex-weighted graphs were first introduced by Bóna, Ju, and Yoshida. We prove a conjecture stating that for any simple connected graph, the numerator polynomial of the Ehrhart series of its graph polytope is palindromic, using Stanley's reciprocity theorem. Furthermore, we introduce hypergraph polytopes and establish that every simple, connected, unimodular hypergraph polytope is an integer polytope. Additionally, for simple connected uniform hypergraph polytopes, we demonstrate that the numerator polynomial of their Ehrhart series is palindromic. |
| title | Proof of a conjecture on graph polytope |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.11970 |