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Facial weak order in hyperplane arrangements

Algebra & Discrete Mathematics

Speaker: Aram Dermenjian, Université du Québec à Montréal.
Location: 1147 Math Science Building
Start time: Mon, Jun 3 2019, 12:10PM

We describe the facial weak order, a poset structure that extends the poset of regions on a central hyperplane arrangement to the set of all faces of the arrangement which was first introduced on the braid arrangements by Krob, Latapy, Novelli, Phan and Schewer. We provide various characterizations of this poset including a local one, a global one, and a geometric one. We then show that the facial weak order is in fact a lattice for simplicial hyperplane arrangements, generalizing a result by Björner, Edelman and Ziegler showing the poset of regions is a lattice for simplicial arrangements.