Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract)
International audience We study the combinatorics of weighted trees from the point of view of tropical algebraic geometry and tropical linear spaces. The set of dissimilarity vectors of weighted trees is contained in the tropical Grassmannian, so we describe here the tropical linear space of a dissi...
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ftccsdartic:oai:HAL:hal-01215099v1 2023-05-15T16:50:13+02:00 Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract) Iriarte Giraldo, Benjamin Department of Mathematics MIT Massachusetts Institute of Technology (MIT) Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel Reykjavik, Iceland 2011 https://hal.inria.fr/hal-01215099 https://hal.inria.fr/hal-01215099/document https://hal.inria.fr/hal-01215099/file/dmAO0134.pdf en eng HAL CCSD Discrete Mathematics and Theoretical Computer Science DMTCS hal-01215099 https://hal.inria.fr/hal-01215099 https://hal.inria.fr/hal-01215099/document https://hal.inria.fr/hal-01215099/file/dmAO0134.pdf 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://hal.inria.fr/hal-01215099 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.375-386 dissimilarity vector tropical linear space tight span weighted tree matroid polytope T-theory [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 ftccsdartic 2020-12-25T18:15:03Z International audience We study the combinatorics of weighted trees from the point of view of tropical algebraic geometry and tropical linear spaces. The set of dissimilarity vectors of weighted trees is contained in the tropical Grassmannian, so we describe here the tropical linear space of a dissimilarity vector and its associated family of matroids. This gives a family of complete flags of tropical linear spaces, where each flag is described by a weighted tree. Nous étudions les propriétés combinatoires des arbres pondérés avec le formalisme de la géométrie tropicale et des espaces linéaires tropicaux. L'ensemble de vecteurs de dissimilarité des arbres pondérés est contenu dans la grassmannienne tropicale, donc nous décrivons ici l'espace linéaire tropical d'un vecteur de dissimilarité et sa famille de matroïdes associée. Cela permet d'obtenir une famille de drapeaux complets d'espaces linéaires tropicaux, où chaque drapeau est décrit par un arbre pondéré. Conference Object Iceland Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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ftccsdartic |
language |
English |
topic |
dissimilarity vector tropical linear space tight span weighted tree matroid polytope T-theory [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
spellingShingle |
dissimilarity vector tropical linear space tight span weighted tree matroid polytope T-theory [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] Iriarte Giraldo, Benjamin Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract) |
topic_facet |
dissimilarity vector tropical linear space tight span weighted tree matroid polytope T-theory [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
description |
International audience We study the combinatorics of weighted trees from the point of view of tropical algebraic geometry and tropical linear spaces. The set of dissimilarity vectors of weighted trees is contained in the tropical Grassmannian, so we describe here the tropical linear space of a dissimilarity vector and its associated family of matroids. This gives a family of complete flags of tropical linear spaces, where each flag is described by a weighted tree. Nous étudions les propriétés combinatoires des arbres pondérés avec le formalisme de la géométrie tropicale et des espaces linéaires tropicaux. L'ensemble de vecteurs de dissimilarité des arbres pondérés est contenu dans la grassmannienne tropicale, donc nous décrivons ici l'espace linéaire tropical d'un vecteur de dissimilarité et sa famille de matroïdes associée. Cela permet d'obtenir une famille de drapeaux complets d'espaces linéaires tropicaux, où chaque drapeau est décrit par un arbre pondéré. |
author2 |
Department of Mathematics MIT Massachusetts Institute of Technology (MIT) Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel |
format |
Conference Object |
author |
Iriarte Giraldo, Benjamin |
author_facet |
Iriarte Giraldo, Benjamin |
author_sort |
Iriarte Giraldo, Benjamin |
title |
Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract) |
title_short |
Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract) |
title_full |
Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract) |
title_fullStr |
Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract) |
title_full_unstemmed |
Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract) |
title_sort |
dissimilarity vectors of trees and their tropical linear spaces (extended abstract) |
publisher |
HAL CCSD |
publishDate |
2011 |
url |
https://hal.inria.fr/hal-01215099 https://hal.inria.fr/hal-01215099/document https://hal.inria.fr/hal-01215099/file/dmAO0134.pdf |
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://hal.inria.fr/hal-01215099 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.375-386 |
op_relation |
hal-01215099 https://hal.inria.fr/hal-01215099 https://hal.inria.fr/hal-01215099/document https://hal.inria.fr/hal-01215099/file/dmAO0134.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1766040390844022784 |