Lattice characterization of cyclic interval hypergraphic posets
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915981340704768 |
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| author | Gélinas, Félix Yang, Yirong |
| author_facet | Gélinas, Félix Yang, Yirong |
| contents | Hypergraphic polytopes $Δ_{\mathbb{H}}$ arise as Minkowski sums of simplices indexed by the hyperedges of a hypergraph $\mathbb{H}$. Orienting the $1$-skeleton of such a polytope by a certain generic linear functional gives rise to the hypergraphic poset $P_{\mathbb{H}}$. Hypergraphic posets include the weak order for the permutahedron and the Tamari lattice for the associahedron. This motivates the problem of determining when $P_{\mathbb{H}}$ is a lattice. In this paper, we give a complete lattice characterization for cyclic interval hypergraphs, extending the result of Bergeron and Pilaud for interval hypergraphs, and the result of Adenbaum et al. for the complete cyclic interval hypergraph. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_03913 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lattice characterization of cyclic interval hypergraphic posets Gélinas, Félix Yang, Yirong Combinatorics 06B10, 52B11, 52B12, 05C65 Hypergraphic polytopes $Δ_{\mathbb{H}}$ arise as Minkowski sums of simplices indexed by the hyperedges of a hypergraph $\mathbb{H}$. Orienting the $1$-skeleton of such a polytope by a certain generic linear functional gives rise to the hypergraphic poset $P_{\mathbb{H}}$. Hypergraphic posets include the weak order for the permutahedron and the Tamari lattice for the associahedron. This motivates the problem of determining when $P_{\mathbb{H}}$ is a lattice. In this paper, we give a complete lattice characterization for cyclic interval hypergraphs, extending the result of Bergeron and Pilaud for interval hypergraphs, and the result of Adenbaum et al. for the complete cyclic interval hypergraph. |
| title | Lattice characterization of cyclic interval hypergraphic posets |
| topic | Combinatorics 06B10, 52B11, 52B12, 05C65 |
| url | https://arxiv.org/abs/2605.03913 |