The Euler discriminant of families of hyperplane complements is the zero set of an explicit product of determinants indexed by connected square subgraphs.
Faces of Cosmological Polytopes
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abstract
A cosmological polytope is a lattice polytope introduced by Arkani-Hamed, Benincasa, and Postnikov in their study of the wavefunction of the universe in a class of cosmological models. More concretely, they construct a cosmological polytope for any Feynman diagram, i.e. an undirected graph. In this paper, we initiate a combinatorial study of these polytopes. We give a complete description of their faces, identify minimal faces that are not simplices and compute the number of faces in specific instances. In particular, we give a recursive description of the $f$-vector of cosmological polytopes of trees.
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Euler Discriminant of Complements of Hyperplanes
The Euler discriminant of families of hyperplane complements is the zero set of an explicit product of determinants indexed by connected square subgraphs.