A new class of magic positive Ehrhart polynomials of reflexive polytopes
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908430233501696 |
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| author | Konoike, Masato |
| author_facet | Konoike, Masato |
| contents | The magic positivity of Ehrhart polynomials is a useful tool for proving the real-rootedness of the $h^\ast$-polynomials. In this paper, we provide a new class of reflexive polytopes whose Ehrhart polynomials are magic positive. First, we prove that the Ehrhart polynomials of Stasheff polytopes are magic positive. Second, we provide a partial proof of the magic positivity of the Ehrhart polynomials of the dual polytopes of the symmetric edge polytopes of cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new class of magic positive Ehrhart polynomials of reflexive polytopes Konoike, Masato Combinatorics Primary: 52B12, Secondary: 05A15, 52B20 The magic positivity of Ehrhart polynomials is a useful tool for proving the real-rootedness of the $h^\ast$-polynomials. In this paper, we provide a new class of reflexive polytopes whose Ehrhart polynomials are magic positive. First, we prove that the Ehrhart polynomials of Stasheff polytopes are magic positive. Second, we provide a partial proof of the magic positivity of the Ehrhart polynomials of the dual polytopes of the symmetric edge polytopes of cycles. |
| title | A new class of magic positive Ehrhart polynomials of reflexive polytopes |
| topic | Combinatorics Primary: 52B12, Secondary: 05A15, 52B20 |
| url | https://arxiv.org/abs/2409.16648 |