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Quotients of positroids and lattice path matroids

Carolina Benedetti

Positroids are a particular class of realizable matroids that are very rich combinatorially. As matroids, one may wonder how to make use of the combinatorics that positroids possess in order to understand whether two given positroids on the same ground set are concordant. That is, can we determine combinatorially if given positroids \(P\) and \(Q\), \(P\) is a quotient of \(Q\), or vice versa? One motivation to understand quotients of positroids arises from a result by Tsukerman and Williams involving flag matroids and Bruhat interval polytopes. We will explore this connection via flags of lattice path matroids (LPMs). In particular, we present a characterization of quotients of LPMs.

This is based on work in progress with K. Knauer.