Reflexive polytopes arising from perfect graphs

Abstract

Reflexive polytopes form one of the distinguished classes of lattice polytopes. Especially reflexive polytopes which possess the integer decomposition property are of interest. In the present paper, by virtue of the algebraic technique on Grönbner bases, a new class of reflexive polytopes which possess the integer decomposition property and which arise from perfect graphs will be presented. Furthermore, the Ehrhart $\delta$-polynomials of these polytopes will be studied.

13 pages

References in corpus (4)

• Centrally symmetric configurations of order polytopes
• Facets and volume of Gorenstein Fano polytopes
• Reverse lexicographic squarefree initial ideals and Gorenstein Fano polytopes
• Quadratic Gröbner bases arising from partially ordered sets

Cited by in corpus (8)

• The $h^{\ast }$-polynomials of locally anti-blocking lattice polytopes and their $\gamma$-positivity
• Integer decomposition property for Cayley sums of order and stable set polytopes
• Reflexive polytopes arising from bipartite graphs with $\gamma$-positivity associated to interior polynomials
• Enriched order polytopes and Enriched Hibi rings
• Enriched chain polytopes
• Reflexive polytopes arising from edge polytopes
• The depth of a reflexive polytope
• Perfectly contractile graphs and quadratic toric rings