IDP for 2-Partition Maximal Symmetric Polytopes

Abstract

We provide a framework for which one can approach showing the integer decomposition property for symmetric polytopes. We utilize this framework to prove a special case which we refer to as $2$-partition maximal polytopes in the case where it lies in a hyperplane of ${\mathbb{R}}^3$. Our method involves proving a special collection of polynomials have saturated Newton polytope.