Séminaire Lotharingien de Combinatoire, 84B.14 (2020), 11 pp.
Aram Dermenjian, Christophe Hohlweg, Thomas McConville and Vincent Pilaud
The Facial Weak Order on Hyperplane Arrangements
Abstract.
We introduce the facial weak order of a real hyperplane
arrangement A. It is a partial order on all faces
of A which naturally extends the poset of regions
of A. We provide various characterizations of the facial
weak order and show that it is a lattice as soon as the poset of
regions is a lattice.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
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