Deformed Graphical Zonotopes

We study deformations of graphical zonotopes. Deformations of the classical permutahedron (which is the graphical zonotope of the complete graph) have been intensively studied in recent years under the name of generalized permutahedra. We provide an irredundant description of the deformation cone of...

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Detalhes bibliográficos
Autores: Padrol Sureda, Arnau, Pilaud, Vincent, Poullot, Germain
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2025
País:España
Recursos:Universidad de Barcelona
Repositório:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/208541
Acesso em linha:https://hdl.handle.net/2445/208541
Access Level:Acceso aberto
Palavra-chave:Politops
Geometria convexa
Polytopes
Convex geometry
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spelling Deformed Graphical ZonotopesPadrol Sureda, ArnauPilaud, VincentPoullot, GermainPolitopsGeometria convexaPolytopesConvex geometryWe study deformations of graphical zonotopes. Deformations of the classical permutahedron (which is the graphical zonotope of the complete graph) have been intensively studied in recent years under the name of generalized permutahedra. We provide an irredundant description of the deformation cone of the graphical zonotope associated to a graph $G$, consisting of independent equations defining its linear span (in terms of non-cliques of $G$ ) and of the inequalities defining its facets (in terms of common neighbors of neighbors in $G$ ). In particular, we deduce that the faces of the standard simplex corresponding to induced cliques in $G$ form a linear basis of the deformation cone, and that the deformation cone is simplicial if and only if $G$ is triangle-free.Springer Verlag2025info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/acceptedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2445/208541Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/https://doi.org/10.1007/s00454-023-00586-xDiscrete & Computational Geometry, 2025https://doi.org/https://doi.org/10.1007/s00454-023-00586-xcc-by (c) Arnau Padrol et al., 2025http://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2085412026-05-27T06:46:51Z
dc.title.none.fl_str_mv Deformed Graphical Zonotopes
title Deformed Graphical Zonotopes
spellingShingle Deformed Graphical Zonotopes
Padrol Sureda, Arnau
Politops
Geometria convexa
Polytopes
Convex geometry
title_short Deformed Graphical Zonotopes
title_full Deformed Graphical Zonotopes
title_fullStr Deformed Graphical Zonotopes
title_full_unstemmed Deformed Graphical Zonotopes
title_sort Deformed Graphical Zonotopes
dc.creator.none.fl_str_mv Padrol Sureda, Arnau
Pilaud, Vincent
Poullot, Germain
author Padrol Sureda, Arnau
author_facet Padrol Sureda, Arnau
Pilaud, Vincent
Poullot, Germain
author_role author
author2 Pilaud, Vincent
Poullot, Germain
author2_role author
author
dc.subject.none.fl_str_mv Politops
Geometria convexa
Polytopes
Convex geometry
topic Politops
Geometria convexa
Polytopes
Convex geometry
description We study deformations of graphical zonotopes. Deformations of the classical permutahedron (which is the graphical zonotope of the complete graph) have been intensively studied in recent years under the name of generalized permutahedra. We provide an irredundant description of the deformation cone of the graphical zonotope associated to a graph $G$, consisting of independent equations defining its linear span (in terms of non-cliques of $G$ ) and of the inequalities defining its facets (in terms of common neighbors of neighbors in $G$ ). In particular, we deduce that the faces of the standard simplex corresponding to induced cliques in $G$ form a linear basis of the deformation cone, and that the deformation cone is simplicial if and only if $G$ is triangle-free.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/acceptedVersion
info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/208541
url https://hdl.handle.net/2445/208541
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/https://doi.org/10.1007/s00454-023-00586-x
Discrete & Computational Geometry, 2025
https://doi.org/https://doi.org/10.1007/s00454-023-00586-x
dc.rights.none.fl_str_mv cc-by (c) Arnau Padrol et al., 2025
http://creativecommons.org/licenses/by/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by (c) Arnau Padrol et al., 2025
http://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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