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arXiv · 2605.03913

Lattice characterization of cyclic interval hypergraphic posets

Félix Gélinas·Yirong Yang
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Abstract

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.

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Félix Gélinas, Yirong Yang. 2026-05-05. Lattice characterization of cyclic interval hypergraphic posets. https://arxiv.org/abs/2605.03913

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