Quotients of uniform positroids

TL;DR

This paper characterizes quotients of uniform positroids using combinatorial methods, specifically decorated permutations, and describes their circuits, advancing understanding of flag positroids within Coxeter matroids.

Contribution

It provides a new combinatorial characterization of quotients of uniform positroids and fully describes their circuits using decorated permutations.

Findings

Characterization of quotients of uniform positroids via decorated permutations

Complete description of circuits in the quotient family

Enhanced understanding of flag positroids in Coxeter matroids

Abstract

Flag matroids are a rich family of Coxeter matroids that can be characterized using pairs of matroids that form a quotient. We consider a class of matroids called positroids, introduced by Postnikov, and utilize their combinatorial representations to explore characterizations of flag positroids. Given a uniform positroid, we give a purely combinatorial characterization of a family of positroids that form quotients with it. We state this in terms of their associated decorated permutations. In proving our characterization we also fully describe the circuits of this family.