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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