Centrally symmetric configurations of integer matrices

Abstract

The concept of centrally symmetric configurations of integer matrices is introduced. We study the problem when the toric ring of a centrally symmetric configuration is normal as well as is Gorenstein. In addition, Gröbner bases of toric ideals of centrally symmetric configurations will be discussed. Special attentions will be given to centrally symmetric configurations of unimodular matrices and those of incidence matrices of finite graphs.

14 pages, 1 figure

Cited by in corpus (16)

• Many faces of symmetric edge polytopes
• Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part
• Interlacing Ehrhart Polynomials of Reflexive Polytopes
• Centrally symmetric configurations of order polytopes
• Symmetric edge polytopes and matching generating polynomials
• Reflexive polytopes arising from perfect graphs
• Toric rings and ideals of stable set polytopes
• The $h^{\ast }$-polynomials of locally anti-blocking lattice polytopes and their $\gamma$-positivity
• A toric deformation method for solving Kuramoto equations
• Reflexive polytopes arising from bipartite graphs with $\gamma$-positivity associated to interior polynomials
• On the gamma-vector of symmetric edge polytopes
• Markov chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations
• Nef-partitions arising from unimodular configurations
• Graph edge contraction and subdivisions for adjacency polytopes
• Unimodular polytopes and column number bounds on polytopal totally unimodular matrices via Seymour's decomposition theorem
• Rigid Gorenstein toric Fano varieties arising from directed graphs