dc.contributor.author
Bergeron, N.
dc.contributor.author
Pilaud, Vincent
dc.date.accessioned
2026-01-20T13:52:07Z
dc.date.available
2026-01-20T13:52:07Z
dc.date.issued
2026-02-01
dc.identifier.uri
http://hdl.handle.net/2072/489145
dc.description.abstract
For a hypergraph H on [n], the hypergraphic poset PH is the transitive closure of the oriented skeleton of the hypergraphic polytope AH (the Minkowski sum of the standard simplices AH for all H is an element of H). Hypergraphic posets include the weak order for the permutahedron (when H is the complete graph on [n]) and the Tamari lattice for the associahedron (when H is the set of all intervals of [n]), which motivates the study of lattice properties of hypergraphic posets. In this paper, we focus on interval hypergraphs, where all hyperedges are intervals of [n]. We characterize the interval hypergraphs I for which PI is a lattice, a distributive lattice, a semidistributive lattice, and a lattice quotient of the weak order.
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dc.description.sponsorship
NB was supported by NSERC and York Research Chair in Applied Algebra. VP was supported by the Spanish project PID2022-137283NB-C21 of MCIN/AEI/10.13039/501100011033/FEDER, UE, by the Spanish-German project COMPOTE (AEI PCI2024-155081-2 & DFG 541393733) , by the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M) , by the Departament de Recerca i Universitats de la Generalitat de Catalunya (2021 SGR 00697) , and by the French-Austrian project PAGCAP (ANR-21-CE48-0020 & FWF I 5788) .
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dc.format.extent
33 p.
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dc.relation.ispartof
European Journal of Combinatorics
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dc.rights
Attribution-NonCommercial 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by-nc/4.0/
*
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
hypergraphs
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dc.title
Interval hypergraphic lattices
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1016/j.ejc.2025.104285
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
