Ehrhart positivity for marked order polytopes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915942305366016 |
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| author | Jochemko, Katharina Menon, Krishna |
| author_facet | Jochemko, Katharina Menon, Krishna |
| contents | Given a pair of finite posets $A \subseteq P$, the function counting integer-valued order preserving extensions of an order preserving map $λ: A\rightarrow \mathbb{Z}$ from $A$ to $P$ is given by a piecewise polynomial in $λ$. We provide a criterion for the nonnegativity of the coefficients of these multivariate polynomials and apply it to show that marked order polytopes of skew shapes are Ehrhart positive in a multivariate sense. This extends recent results of Ferroni-Morales-Panova on order polytopes of skew shapes and proves conjectures on the Ehrhart positivity of skew Gelfand-Tsetlin polytopes and $m$-generalized Pitman-Stanley polytopes due to Alexanderson-Alhajjar and Dugan-Hegarty-Morales-Raymond, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08394 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ehrhart positivity for marked order polytopes Jochemko, Katharina Menon, Krishna Combinatorics 05A17, 06A07, 52B12, 52B20 Given a pair of finite posets $A \subseteq P$, the function counting integer-valued order preserving extensions of an order preserving map $λ: A\rightarrow \mathbb{Z}$ from $A$ to $P$ is given by a piecewise polynomial in $λ$. We provide a criterion for the nonnegativity of the coefficients of these multivariate polynomials and apply it to show that marked order polytopes of skew shapes are Ehrhart positive in a multivariate sense. This extends recent results of Ferroni-Morales-Panova on order polytopes of skew shapes and proves conjectures on the Ehrhart positivity of skew Gelfand-Tsetlin polytopes and $m$-generalized Pitman-Stanley polytopes due to Alexanderson-Alhajjar and Dugan-Hegarty-Morales-Raymond, respectively. |
| title | Ehrhart positivity for marked order polytopes |
| topic | Combinatorics 05A17, 06A07, 52B12, 52B20 |
| url | https://arxiv.org/abs/2604.08394 |