The facial weak order on hyperplane arrangements - Laboratoire d'informatique de l'X (LIX) Accéder directement au contenu
Article Dans Une Revue Discrete and Computational Geometry Année : 2022

The facial weak order on hyperplane arrangements

Résumé

We extend the facial weak order from finite Coxeter groups to central hyperplane arrangements. The facial weak order extends the poset of regions of a hyperplane arrangement to all its faces. We provide four non-trivially equivalent definitions of the facial weak order of a central arrangement: (1) by exploiting the fact that the faces are intervals in the poset of regions, (2) by describing its cover relations, (3) using covectors of the corresponding oriented matroid, and (4) using certain sets of normal vectors closely related to the geometry of the corresponding zonotope. Using these equivalent descriptions, we show that when the poset of regions is a lattice, the facial weak order is a lattice. In the case of simplicial arrangements, we further show that this lattice is semidistributive and give a description of its join-irreducible elements. Finally, we determine the homotopy type of all intervals in the facial weak order.
Fichier principal
Vignette du fichier
paper.pdf (513.11 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02997625 , version 1 (10-11-2020)

Identifiants

Citer

Aram Dermenjian, Christophe Hohlweg, Thomas Mcconville, Vincent Pilaud. The facial weak order on hyperplane arrangements. Discrete and Computational Geometry, 2022, 67, pp.166-202. ⟨hal-02997625⟩
18 Consultations
47 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More