Combinatorics Seminar: "Birkhoff polytopes of different type and the orthant-lattice property"

Abstract: Given a d-dimensional lattice polytope P, we say that P has the orthant-lattice property (OLP) if the subpolytope obtained by restriction to any orthant is a lattice polytope. While this property feels somewhat contrived, it can actually be quite useful in verification of discrete geometric properties of P. In this talk, we will discuss a number of results for the existence of triangulation and the integer decomposition property for reflexive OLP polytopes. One such polytope which fits into the program is a type-B analogue of the Birkhoff polytope and its dual polytope, the investigation of which led to interest in this property.

This is based on joint work with Florian Kohl (Aalto University).

Host: Laura Escobar Vega