Work

The weak order on integer posets

Year: 2019

Type: article

Abstract: We explore lattice structures on integer binary relations (i.e. binary relations on the set { 1 , 2 , ⋯ , n } for a fixed integer n ) and on integer posets (i.e. partial orders on the set { 1 , 2 , ⋯ , n } for a fixed integer n ). We first observe that the weak order on the symmetric group naturally extends to a lattice structure on all integer binary relations. We then show that the subposet of this weak order induced by integer posets defines as well a lattice. We finally study the subposets of this weak order induced by specific families of integer posets corresponding to the elements, the intervals, and the faces of the permutahedron, the associahedron, and some recent generalizations of those.

Source: Algebraic Combinatorics

DOI: 10.5802/alco.36

Authors: Grégory Chatel, Vincent Pilaud, Viviane Pons

Institutions: Laboratoire d'Informatique Gaspard-Monge, Université Gustave Eiffel, Laboratoire d'Informatique de l'École Polytechnique, Université Paris-Sud, Laboratoire de Recherche en Informatique

Language: Latvian

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Awards: G3032270807, Surfaces, Categorification and Combinatorics of Cluster Algebras