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arXiv · 1701.05529

On lattice path matroid polytopes: integer points and Ehrhart polynomial

Kolja Knauer·Leonardo Martínez-Sandoval·Jorge Luis Ramírez Alfonsín
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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.

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Kolja Knauer, Leonardo Martínez-Sandoval, Jorge Luis Ramírez Alfonsín. 2017-01-19. On lattice path matroid polytopes: integer points and Ehrhart polynomial. https://arxiv.org/abs/1701.05529

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