Algebraic and Enumerative Combinatorics Seminar - Jerónimo Valencia-Porras

Thursday, November 2, 2023 2:00 pm - 2:00 pm EDT (GMT -04:00)

Title: Snake decompositions of lattice path matroids

Speaker: Jerónimo Valencia-Porras
Affiliation: University of Waterloo
Location: MC 6029

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:00 pm.

Abstract: We study Ehrhart theory of lattice path matroid polytopes motivated by a conjecture by De Loera, Haws and Köppe. More specifically, we aim to understand the h*-vector of this family of matroid polytopes. To do so, we subdivide them into smaller matroid polytopes such that each piece is a snake, which are matroids such that their matroid polytope coincides with the order polytope of a fence poset. Together with the triangulation of order polytopes given by Stanley, we give a combinatorial interpretation for the h*-vector of lattice path matroid polytopes. For the special case of Schubert matroids of rank 2 we go one step further and prove that these h*-vectors count permutations with one descent filtered by initial gaps, and prove a recurrence relation for their volumes.

This talk is based in joint work with Carolina Benedetti and Kolja Knauer.