Compatibility fans realizing graphical nested complexes
Graph associahedra are polytopes realizing the nested complex N(G) on connected subgraphs of a graph G.While all known explicit constructions produce polytopes with the same normal fan, the great variety of fan realizationsof classical associahedra and the analogy between finite type cluster complex...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/6400/pdf |
| _version_ | 1797270230127345664 |
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| author | Thibault Manneville Vincent Pilaud |
| author_facet | Thibault Manneville Vincent Pilaud |
| author_sort | Thibault Manneville |
| collection | DOAJ |
| description | Graph associahedra are polytopes realizing the nested complex N(G) on connected subgraphs of a graph G.While all known explicit constructions produce polytopes with the same normal fan, the great variety of fan realizationsof classical associahedra and the analogy between finite type cluster complexes and nested complexes incitedus to transpose S. Fomin and A. Zelevinsky's construction of compatibility fans for generalized associahedra (2003)to graph associahedra. Using a compatibility degree, we construct one fan realization of N(G) for each of its facets.Specifying G to paths and cycles, we recover a construction by F. Santos for classical associahedra (2011) and extendF. Chapoton, S. Fomin and A. Zelevinsky's construction (2002) for type B and C generalized associahedra. |
| first_indexed | 2024-04-25T02:00:58Z |
| format | Article |
| id | doaj.art-b7398bd6bd1d49d0ad133a8f46926d04 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:58Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-b7398bd6bd1d49d0ad133a8f46926d042024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.64006400Compatibility fans realizing graphical nested complexesThibault Manneville0Vincent Pilaud1https://orcid.org/0000-0002-2070-9223Laboratoire d'informatique de l'École polytechnique [Palaiseau]Laboratoire d'informatique de l'École polytechnique [Palaiseau]Graph associahedra are polytopes realizing the nested complex N(G) on connected subgraphs of a graph G.While all known explicit constructions produce polytopes with the same normal fan, the great variety of fan realizationsof classical associahedra and the analogy between finite type cluster complexes and nested complexes incitedus to transpose S. Fomin and A. Zelevinsky's construction of compatibility fans for generalized associahedra (2003)to graph associahedra. Using a compatibility degree, we construct one fan realization of N(G) for each of its facets.Specifying G to paths and cycles, we recover a construction by F. Santos for classical associahedra (2011) and extendF. Chapoton, S. Fomin and A. Zelevinsky's construction (2002) for type B and C generalized associahedra.https://dmtcs.episciences.org/6400/pdfcombinatorics[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Thibault Manneville Vincent Pilaud Compatibility fans realizing graphical nested complexes Discrete Mathematics & Theoretical Computer Science combinatorics [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Compatibility fans realizing graphical nested complexes |
| title_full | Compatibility fans realizing graphical nested complexes |
| title_fullStr | Compatibility fans realizing graphical nested complexes |
| title_full_unstemmed | Compatibility fans realizing graphical nested complexes |
| title_short | Compatibility fans realizing graphical nested complexes |
| title_sort | compatibility fans realizing graphical nested complexes |
| topic | combinatorics [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6400/pdf |
| work_keys_str_mv | AT thibaultmanneville compatibilityfansrealizinggraphicalnestedcomplexes AT vincentpilaud compatibilityfansrealizinggraphicalnestedcomplexes |