Centrally symmetric configurations of order polytopes

TL;DR

This paper proves that the toric ideal of the centrally symmetric configuration of an order polytope has a squarefree quadratic initial ideal, leading to the convex polytope being a normal Gorenstein Fano polytope, revealing new geometric properties.

Contribution

It establishes the existence of a squarefree quadratic initial ideal for the toric ideal of centrally symmetric order polytope configurations and characterizes the resulting convex polytope.

Findings

Toric ideal has a squarefree quadratic initial ideal

Resulting polytope is a normal Gorenstein Fano polytope

Provides new insights into the geometry of order polytope configurations

Abstract

It is shown that the toric ideal of the centrally symmetric configuration of the order polytope of a finite partially ordered set possesses a squarefree quadratic initial ideal. It then follows that the convex polytope arising from the centrally symmetric configuration of an order polytope is a normal Gorenstein Fano polytope.