Reverse lexicographic squarefree initial ideals and Gorenstein Fano polytopes

TL;DR

This paper introduces a new class of Gorenstein Fano polytopes derived from stable set polytopes of perfect graphs using reverse lexicographic squarefree initial ideals of toric ideals.

Contribution

It establishes a novel connection between toric ideals, perfect graphs, and Gorenstein Fano polytopes through algebraic and combinatorial methods.

Findings

New class of Gorenstein Fano polytopes identified

Connection between stable set polytopes and reflexive polytopes established

Application of reverse lexicographic squarefree initial ideals demonstrated

Abstract

Via the theory of reverse lexicographic squarefree initial ideals of toric ideals, we give a new class of Gorenstein Fano polytopes (reflexive polytopes) arising from a pair of stable set polytopes of perfect graphs.