University of Minnesota Combinatorics Seminar
Friday, November 5, 2010
3:35pm in 570 Vincent Hall



Lattice Path Matroid Polytopes

Hoda Bidkhori

North Carolina State University


Abstract

This talk concerns lattice path matroid polytopes. The theory of matroid polytopes has gained prominence due to its applications in algebraic geometry, combinatorial optimization, Coxeter group theory, and, most recently, tropical geometry. In general matroid polytopes are not well understood.

Lattice path matroid polytopes belong to two famous classes of polytopes, sorted closed matroid polytopes and polypositroids. We study several properties of LPMPs and build a new connection between the theories of matroid polytopes and lattice paths. I investigate many properties of LPMPs, including their face structure, decomposition, and triangulations, as well as formulas for calculating their Ehrhart polynomial and volume.