On lattice path matroid polytopes: integer points and Ehrhart polynomial
Combinatorics
2017-10-26 v2
Abstract
In this paper we investigate the number of integer points lying in dilations of lattice path matroid polytopes. We give a characterization of such points as polygonal paths in the diagram of the lattice path matroid. Furthermore, we prove that lattice path matroid polytopes are affinely equivalent to a family of distributive polytopes. As applications we obtain two new infinite families of matroids verifying a conjecture of De Loera et.~al. and present an explicit formula of the Ehrhart polynomial for one of them.
Keywords
Cite
@article{arxiv.1701.05529,
title = {On lattice path matroid polytopes: integer points and Ehrhart polynomial},
author = {Kolja Knauer and Leonardo Martínez-Sandoval and Jorge Luis Ramírez Alfonsín},
journal= {arXiv preprint arXiv:1701.05529},
year = {2017}
}
Comments
23 pages, 13 figures, minor corrections