The $h^{*}$-polynomial of the cut polytope of $K_{2,m}$ in the lattice spanned by its vertices

zbMath1444.05071arXiv1904.10667MaRDI QIDQ3300676

Ryuichi Sakamoto

Publication date: 29 July 2020

Full work available at URL: https://arxiv.org/abs/1904.10667

zbMATH Keywords

Gröbner basiscomplete bipartite graphcut polytope\(h^\ast\)-polynomial

Mathematics Subject Classification ID

Graph polynomials (05C31) Exact enumeration problems, generating functions (05A15) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Cites Work

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• Cut ideals of \(K_{4}\)-minor free graphs are generated by quadrics
• Properties of cut ideals associated to ring graphs
• On Hilbert bases of cuts
• Normality of cut polytopes of graphs is a minor closed property
• Markov bases of binary graph models of \(K_{4}\)-minor free graphs
• Two poset polytopes
• Polynômes arithmétiques et méthode des polyedres en combinatoire
• A lower bound theorem for Ehrhart polynomials of convex polytopes
• \(h^\ast\)-vectors, Eulerian polynomials and stable polytopes of graphs
• Lexicographic and reverse lexicographic quadratic Gröbner bases of cut ideals
• Gorenstein cut polytopes
• Strong Koszulness of the toric ring associated to a cut ideal
• Polytopes, Rings, and K-Theory
• Decompositions of Rational Convex Polytopes
• Binomial Ideals
• Ehrhart Theory of Spanning Lattice Polytopes
• Computing the Continuous Discretely
• Eulerian Numbers