Séminaire Lotharingien de Combinatoire, 80B.70 (2018), 12 pp.

Carolina Benedetti, Nantel Bergeron, and John Machacek

Hypergraphic Polytopes: Combinatorial Properties and Antipode

Abstract. Given a hypergraph G, its hypergraphic polytope PG is the Minkowski sum of simplices corresponding to each hyperedge of G. Using a notion of orientation on G, we prove that the faces of PG are in bijective correspondence with acyclic orientations of G. This allows us to give a geometric understanding of the antipode in a cocommutative Hopf algebra of hypergraphs. We also give a characterization of when a hypergraphic polytope is a simple polytope. The correspondence between faces and acyclic orientations is used to prove some combinatorial properties of nestohedra and generalized Pitman-Stanley polytopes.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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