Anastasia Chavez: Characterizing quotients of positroids

Abstract

We characterize quotients of specific families of positroids. Positroids are a special class of representable matroids introduced by Postnikov in the study of the nonnegative part of the Grassmannian. Postnikov defined several combinatorial objects that index positroids. In this talk, we make use of two of these objects to combinatorially characterize when certain positroids are quotients. Furthermore, we conjecture a general rule for quotients among arbitrary positroids on the same ground set. This is joint work with Carolina Benedetti and Daniel Tamayo.