Term rewriting on nestohedra
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929682665963520 |
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| author | Curien, Pierre-Louis Laplante-Anfossi, Guillaume |
| author_facet | Curien, Pierre-Louis Laplante-Anfossi, Guillaume |
| contents | We define term rewriting systems on the vertices and faces of nestohedra, and show that the former are confluent and terminating. While the associated posets on vertices generalize Barnard--McConville's flip order for graph-associahedra, the preorders on faces generalize the facial weak order for permutahedra and the generalized Tamari order for associahedra. Moreover, we define and study contextual families of nestohedra, whose local confluence diagrams satisfy a certain uniformity condition. Among them are associahedra and operahedra, whose associated proofs of confluence for their rewriting systems reproduce proofs of categorical coherence theorems for monoidal categories and categorified operads. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Term rewriting on nestohedra Curien, Pierre-Louis Laplante-Anfossi, Guillaume Category Theory Logic in Computer Science Algebraic Topology Combinatorics 68Q42 (Primary) 18N20, 52B11 (Secondary) We define term rewriting systems on the vertices and faces of nestohedra, and show that the former are confluent and terminating. While the associated posets on vertices generalize Barnard--McConville's flip order for graph-associahedra, the preorders on faces generalize the facial weak order for permutahedra and the generalized Tamari order for associahedra. Moreover, we define and study contextual families of nestohedra, whose local confluence diagrams satisfy a certain uniformity condition. Among them are associahedra and operahedra, whose associated proofs of confluence for their rewriting systems reproduce proofs of categorical coherence theorems for monoidal categories and categorified operads. |
| title | Term rewriting on nestohedra |
| topic | Category Theory Logic in Computer Science Algebraic Topology Combinatorics 68Q42 (Primary) 18N20, 52B11 (Secondary) |
| url | https://arxiv.org/abs/2403.15987 |