# Cycle algebras and polytopes of matroids

@inproceedings{Romer2021CycleAA, title={Cycle algebras and polytopes of matroids}, author={Tim Romer and Sara Saeedi Madani}, year={2021} }

Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an algebraic and geometric investigation of these polytopes by studying their toric algebras, called cycle algebras, and their defining ideals. Several matroid operations are considered which determine faces of cycle polytopes that belong again to this class of…

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