Jerónimo Valencia-Porras:Snake decomposition of lattice path matroids

Abstract: Lattice path matroids (LPMs) are positroids whose base polytopes have a nice decomposition. We provide a geometric perspective to this decomposition in terms of fences and their order polytopes, which correspond to a certain class of LPMs we call snakes. This gives an explicit description of an unimodular triangulation of the matroid base polytope of the LPM. Moreover, restricting to the case of LPMs of rank 2, we obtain a combinatorial interpretation for the h*-vector of these polytopes and recursive formulas for their volume. We also characterize Gorenstein LPMs, which henceforth have unimodal h*-vector. This is joint work with Carolina Benedetti-Velásquez and Kolja Knauer.