Quotients of lattice path matroids

Abstract: Matroids are a combinatorial object that generalize the notion of linear independence. One way to characterize matroids is via polytopes, as shown in the work of Gelfand, Goresky, MacPherson, Serganova.

In this talk we will focus on a particular class of matroids called Lattice Path Matroids (LPMs). We will show when a collection M_1,...,M_k of LPMs are a flag matroid, using their combinatorics. Part of our work will show that the polytope associated to such a flag can be thought as an interval in the Bruhat order, and thus provides a partial understanding of flags of LPMs from a polytopal point of view.

We will not assume previous knowledge on matroids nor quotients. This is joint work with Kolja Knauer.

algebraic geometrycombinatorics

Audience: researchers in the topic

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Algebra, Geometry, and Combinatorics

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