Speaker:  George Nasr, Augustana University

Title:  IDP for 2-Partition Maximal Symmetric Polytopes

Abstract:

The Integer Decomposition Property (IDP) for a polytope P essentially asks if the points in any scaled version of a polytope can be written as a sum of points in P itself. Despite a seemingly trite definition, asking if a polytope has IDP is among the many popular problems in discrete mathematics that has a breadth of applications, from solving other questions in discrete mathematics like understanding Ehrhart polynomials, to understanding properties of abstractly defined algebraic structures associated to polytopes, to optimization for integer programing problems whose constraints define a polytope. 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 R^3. Our method involves proving a special collection of polynomials have saturated Newton polytope.