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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