Many faces of symmetric edge polytopes

Abstract

Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple graphs. In the present paper we highlight their connections to the Kuramoto synchronization model in physics -- where they are called adjacency polytopes -- and to Kantorovich--Rubinstein polytopes from finite metric space theory. Each of these connections motivates the study of symmetric edge polytopes of particular classes of graphs. We focus on such classes and apply algebraic-combinatorial methods to investigate invariants of the associated symmetric edge polytopes.

arXiv comment35 pages, 8 figures. Comments are very welcome!

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Cited by in corpus (10)

• Symmetric edge polytopes and matching generating polynomials
• The $h^{\ast }$-polynomials of locally anti-blocking lattice polytopes and their $\gamma$-positivity
• PQ-type adjacency polytopes of join graphs
• On the gamma-vector of symmetric edge polytopes
• Multivariate volume, Ehrhart, and $h^{\ast }$-polynomials of polytropes
• Facets of Random Symmetric Edge Polytopes, Degree Sequences, and Clustering
• $h^{\ast }$-vectors of graph polytopes using activities of dissecting spanning trees
• Normalized Volumes of Type-PQ Adjacency Polytopes for Certain Classes of Graphs
• On the root count of algebraic Kuramoto equations in cycle networks with uniform coupling
• Rigid Gorenstein toric Fano varieties arising from directed graphs