The brick polytope of a sorting network
International audience The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. Pseudotriangulations and multitriangulations generalize triangulations in two different ways, which have been unified by Pilaud and Pocchiola in their study of pseudoline a...
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ftunivparis:oai:HAL:hal-01215072v1 2024-05-19T07:42:55+00:00 The brick polytope of a sorting network Pilaud, Vincent Santos, Francisco Laboratoire d'informatique de l'École polytechnique Palaiseau (LIX) École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) Université Paris Diderot - Paris 7 (UPD7) Departamento de Matemáticas, Estadística y Computación (MATESCO) Universidad de Cantabria Santander Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel Reykjavik, Iceland 2011 https://inria.hal.science/hal-01215072 https://inria.hal.science/hal-01215072/document https://inria.hal.science/hal-01215072/file/dmAO0168.pdf https://doi.org/10.46298/dmtcs.2952 en eng HAL CCSD Discrete Mathematics and Theoretical Computer Science DMTCS info:eu-repo/semantics/altIdentifier/doi/10.46298/dmtcs.2952 hal-01215072 https://inria.hal.science/hal-01215072 https://inria.hal.science/hal-01215072/document https://inria.hal.science/hal-01215072/file/dmAO0168.pdf doi:10.46298/dmtcs.2952 info:eu-repo/semantics/OpenAccess ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://inria.hal.science/hal-01215072 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.777-788, ⟨10.46298/dmtcs.2952⟩ associahedron sorting networks pseudoline arrangements with contacts [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] info:eu-repo/semantics/conferenceObject Conference papers 2011 ftunivparis https://doi.org/10.46298/dmtcs.2952 2024-04-23T03:52:54Z International audience The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. Pseudotriangulations and multitriangulations generalize triangulations in two different ways, which have been unified by Pilaud and Pocchiola in their study of pseudoline arrangements with contacts supported by a given network. In this paper, we construct the "brick polytope'' of a network, obtained as the convex hull of the "brick vectors'' associated to each pseudoline arrangement supported by the network. We characterize its vertices, describe its faces, and decompose it as a Minkowski sum of simpler polytopes. Our brick polytopes include Hohlweg and Lange's many realizations of the associahedron, which arise as brick polytopes of certain well-chosen networks. L'associaèdre est un polytope dont le graphe est le graphe des flips sur les triangulations d'un polygone convexe. Les pseudotriangulations et les multitriangulations généralisent les triangulations dans deux directions différentes, qui ont été unifiées par Pilaud et Pocchiola au travers de leur étude des arrangements de pseudodroites avec contacts couvrant un support donné. Nous construisons ici le "polytope de briques'' d'un support, obtenu comme l'enveloppe convexe des "vecteurs de briques'' associés à chaque arrangement de pseudodroites couvrant ce support. Nous caractérisons les sommets de ce polytope, décrivons ses faces et le décomposons en somme de Minkowski de polytopes élémentaires. Notre construction contient toutes les réalisations de l'associaèdre d'Hohlweg et Lange, qui apparaissent comme polytopes de briques de certains supports bien choisis. Conference Object Iceland Université de Paris: Portail HAL Discrete Mathematics & Theoretical Computer Science DMTCS Proceeding Proceedings |
institution |
Open Polar |
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Université de Paris: Portail HAL |
op_collection_id |
ftunivparis |
language |
English |
topic |
associahedron sorting networks pseudoline arrangements with contacts [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
spellingShingle |
associahedron sorting networks pseudoline arrangements with contacts [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] Pilaud, Vincent Santos, Francisco The brick polytope of a sorting network |
topic_facet |
associahedron sorting networks pseudoline arrangements with contacts [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
description |
International audience The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. Pseudotriangulations and multitriangulations generalize triangulations in two different ways, which have been unified by Pilaud and Pocchiola in their study of pseudoline arrangements with contacts supported by a given network. In this paper, we construct the "brick polytope'' of a network, obtained as the convex hull of the "brick vectors'' associated to each pseudoline arrangement supported by the network. We characterize its vertices, describe its faces, and decompose it as a Minkowski sum of simpler polytopes. Our brick polytopes include Hohlweg and Lange's many realizations of the associahedron, which arise as brick polytopes of certain well-chosen networks. L'associaèdre est un polytope dont le graphe est le graphe des flips sur les triangulations d'un polygone convexe. Les pseudotriangulations et les multitriangulations généralisent les triangulations dans deux directions différentes, qui ont été unifiées par Pilaud et Pocchiola au travers de leur étude des arrangements de pseudodroites avec contacts couvrant un support donné. Nous construisons ici le "polytope de briques'' d'un support, obtenu comme l'enveloppe convexe des "vecteurs de briques'' associés à chaque arrangement de pseudodroites couvrant ce support. Nous caractérisons les sommets de ce polytope, décrivons ses faces et le décomposons en somme de Minkowski de polytopes élémentaires. Notre construction contient toutes les réalisations de l'associaèdre d'Hohlweg et Lange, qui apparaissent comme polytopes de briques de certains supports bien choisis. |
author2 |
Laboratoire d'informatique de l'École polytechnique Palaiseau (LIX) École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) Université Paris Diderot - Paris 7 (UPD7) Departamento de Matemáticas, Estadística y Computación (MATESCO) Universidad de Cantabria Santander Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel |
format |
Conference Object |
author |
Pilaud, Vincent Santos, Francisco |
author_facet |
Pilaud, Vincent Santos, Francisco |
author_sort |
Pilaud, Vincent |
title |
The brick polytope of a sorting network |
title_short |
The brick polytope of a sorting network |
title_full |
The brick polytope of a sorting network |
title_fullStr |
The brick polytope of a sorting network |
title_full_unstemmed |
The brick polytope of a sorting network |
title_sort |
brick polytope of a sorting network |
publisher |
HAL CCSD |
publishDate |
2011 |
url |
https://inria.hal.science/hal-01215072 https://inria.hal.science/hal-01215072/document https://inria.hal.science/hal-01215072/file/dmAO0168.pdf https://doi.org/10.46298/dmtcs.2952 |
op_coverage |
Reykjavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://inria.hal.science/hal-01215072 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.777-788, ⟨10.46298/dmtcs.2952⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.46298/dmtcs.2952 hal-01215072 https://inria.hal.science/hal-01215072 https://inria.hal.science/hal-01215072/document https://inria.hal.science/hal-01215072/file/dmAO0168.pdf doi:10.46298/dmtcs.2952 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.46298/dmtcs.2952 |
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Discrete Mathematics & Theoretical Computer Science |
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DMTCS Proceeding |
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