Séminaire Lotharingien de Combinatoire, 93B.71 (2025), 12 pp.
Adrien Segovia
(P,φ)-Tamari Lattices
Abstract.
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 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.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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