6 papers
Extremality in semidistributive lattices
Adrien Segovia
We establish several independent results concerning extremal, left modular, congruence uniform, and semidistributive lattices. An equivalent characterization of left modular lattic…
Dimension of unicycle posets
Antoine Abram, Adrien Segovia
Motivated by the study of the dimension of random posets, it was conjectured by Bollobás and Brightwell in 1997 that if is a finite poset whose cover graph contains at most on…
-Tamari and higher torsion lattices of type
Adrien Segovia
The goal of this work is to study the combinatorics of the lattices of higher torsion classes of the higher Auslander and Nakayama algebras of type \textbf{A}. Combinatorial descri…
-Tamari lattices
Adrien Segovia
Given any poset and chain in , we define the -Tamari lattice. We study in depth these lattices and prove in particular that they are join-semidistributive, join…
Rowmotion and Echelonmotion
Colin Defant, Yuhan Jiang, Rene Marczinzik +4
Given a linear extension of a finite poset , we consider the permutation matrix indexing the Schubert cell containing the Cartan matrix of with respect to . This yi…
The free and parking quasi-symmetrizing actions
Adrien Segovia
We define two actions of the infinite symmetric group on the set of words on positive integers, called the free and parking quasi-symmetrizing actions, whose invariants are respect…