English

Lattice characterization of cyclic interval hypergraphic posets

Combinatorics 2026-05-06 v1

Abstract

Hypergraphic polytopes ΔH\Delta_{\mathbb{H}} arise as Minkowski sums of simplices indexed by the hyperedges of a hypergraph H\mathbb{H}. Orienting the 11-skeleton of such a polytope by a certain generic linear functional gives rise to the hypergraphic poset PHP_{\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 PHP_{\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.

Keywords

Cite

@article{arxiv.2605.03913,
  title  = {Lattice characterization of cyclic interval hypergraphic posets},
  author = {Félix Gélinas and Yirong Yang},
  journal= {arXiv preprint arXiv:2605.03913},
  year   = {2026}
}

Comments

18 pages, 9 figures

R2 v1 2026-07-01T12:51:06.695Z