$(P,ϕ)$-Tamari lattices
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916994847080448 |
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| author | Segovia, Adrien |
| author_facet | Segovia, Adrien |
| contents | Given any poset $P$ and chain $ϕ$ in $P$, we define the $(P,ϕ)$-Tamari lattice. We study in depth these lattices and prove in particular that they are join-semidistributive, join-congruence uniform and left modular. We prove that the lattices of higher torsion classes of the higher Auslander and Nakayama algebras of type $\mathbb{A}$ are examples of $(P,ϕ)$-Tamari lattices and thus they inherit their properties. We also give general results related to left modular, extremal and congruence normal lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $(P,ϕ)$-Tamari lattices Segovia, Adrien Combinatorics Given any poset $P$ and chain $ϕ$ in $P$, we define the $(P,ϕ)$-Tamari lattice. We study in depth these lattices and prove in particular that they are join-semidistributive, join-congruence uniform and left modular. We prove that the lattices of higher torsion classes of the higher Auslander and Nakayama algebras of type $\mathbb{A}$ are examples of $(P,ϕ)$-Tamari lattices and thus they inherit their properties. We also give general results related to left modular, extremal and congruence normal lattices. |
| title | $(P,ϕ)$-Tamari lattices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.06088 |