On lattice path matroid polytopes: integer points and Ehrhart polynomial

Kolja Knauer (1, 2) , Leonardo Martínez-Sandoval (3, 4) , Jorge Luis Ramírez Alfonsín (3)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille
2 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle
3 IMAG - Institut Montpelliérain Alexander Grothendieck
4 Instituto de Matematicas [México]

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 poly-topes 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.

Domaines: Informatique [cs]

Kolja Knauer, Leonardo Martínez-Sandoval, Jorge Luis Ramírez Alfonsín. On lattice path matroid polytopes: integer points and Ehrhart polynomial. 2017. ⟨hal-01457185⟩