Geodesic
Hypergraphic Polytopes: Combinatorial Properties and Antipode
Séminaire lotharingien de combinatoire, 80B (2018)

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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. 

@article{SLC_2018_80B_a69,
     author = {Carolina Benedetti and Nantel Bergeron, and John Machacek},
     title = {Hypergraphic {Polytopes:} {Combinatorial} {Properties} and {Antipode}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a69/}
}
TY  - JOUR
AU  - Carolina Benedetti
AU  - Nantel Bergeron,
AU  - John Machacek
TI  - Hypergraphic Polytopes: Combinatorial Properties and Antipode
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a69/
ID  - SLC_2018_80B_a69
ER  - 
%0 Journal Article
%A Carolina Benedetti
%A Nantel Bergeron,
%A John Machacek
%T Hypergraphic Polytopes: Combinatorial Properties and Antipode
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a69/
%F SLC_2018_80B_a69
Carolina Benedetti; Nantel Bergeron,; John Machacek. Hypergraphic Polytopes: Combinatorial Properties and Antipode. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a69/