Chainlink Polytopes and Ehrhart-Equivalence
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913778650578944 |
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| author | Oğuz, Ezgi Kantarcı Özel, Cem Yalım Ravichandran, Mohan |
| author_facet | Oğuz, Ezgi Kantarcı Özel, Cem Yalım Ravichandran, Mohan |
| contents | We introduce a class of polytopes that we call chainlink polytopes and which allow us to construct infinite families of pairs of non isomorphic rational polytopes with the same Ehrhart quasi-polynomial. Our construction is based on circular fence posets, which admit a non-obvious and non-trivial symmetry in their rank sequences that turns out to be reflected in the polytope level. We introduce the related class of chainlink posets and show that they exhibit the same symmetry properties. We further prove an outstanding conjecture on the unimodality of circular rank polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08382 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Chainlink Polytopes and Ehrhart-Equivalence Oğuz, Ezgi Kantarcı Özel, Cem Yalım Ravichandran, Mohan Combinatorics We introduce a class of polytopes that we call chainlink polytopes and which allow us to construct infinite families of pairs of non isomorphic rational polytopes with the same Ehrhart quasi-polynomial. Our construction is based on circular fence posets, which admit a non-obvious and non-trivial symmetry in their rank sequences that turns out to be reflected in the polytope level. We introduce the related class of chainlink posets and show that they exhibit the same symmetry properties. We further prove an outstanding conjecture on the unimodality of circular rank polynomials. |
| title | Chainlink Polytopes and Ehrhart-Equivalence |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2211.08382 |