Title:  r-Stable Hypersimplices

Abstract:  The n,k-hypersimplices are a well-studied collection of polytopes.  Inside each n,k-hypersimplex we can define a finite nesting of subpolytopes that we call the r-stable n,k-hypersimplices.  In this talk, we will define the r-stable hypersimplices and then see that they share a nice geometric relationship via a well-known regular unimodular triangulation of the n,k-hypersimplex in which they live.  Using this relationship, we will then identify some geometric and combinatorial properties of the r-stable hypersimplices.  In doing so, we will see that a number of the properties of the n,k-hypersimplex also hold for the r-stable hypersimplices within.