Work

On linear intervals in the alt \(\nu\)-Tamari lattices

Year: 2024

Type: article

Abstract: Given a lattice path \(\nu\), the \(\nu\)-Tamari lattice and the \(\nu\)-Dyck lattice are two natural examples of partial order structures on the set of lattice paths that lie weakly above \(\nu\). In this paper, we introduce a more general family of lattices, called alt \(\nu\)-Tamari lattices, which contains these two examples as particular cases. Unexpectedly, we show that all these lattices have the same number of linear intervals.Mathematics Subject Classifications: 06A07, 06B05, 05A19Keywords: Lattices, intervals, Tamari

Source: Combinatorial Theory

DOI: 10.5070/c64264254

Authors: Cesar Ceballos, Clément Chenevière

Institutions: Graz University of Technology, Université Paris-Saclay, Institut de Recherche Mathématique Avancée, Université de Strasbourg

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Agence Nationale de la Recherche, Austrian Science Fund