Discrete & Computational Geometry

, Volume 60, Issue 3, pp 698–719 | Cite as

On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial

  • Kolja KnauerEmail author
  • Leonardo Martínez-Sandoval
  • Jorge Luis Ramírez Alfonsín


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.


Ehrhart polynomial Distributive polytope Matroid base polytope Lattice path matroid 



The first author was partially supported by ANR Grants GATO ANR-16-CE40-0009-01 and CAPPS ANR-17-CE40-0018. The second author was supported by the Israel Science Foundation Grant No. 1452/15 and the European Research Council H2020 programme Grant No. 678765. The last two authors were partially supported by ECOS Nord Project M13M01.


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Authors and Affiliations

  1. 1.Laboratoire d’Informatique Fondamentale, Faculté des Sciences de LuminyAix-Marseille Université and CNRSMarseille Cedex 9France
  2. 2.Department of Computer Science, Faculty of Natural SciencesBen-Gurion University of the NegevBeer ShevaIsrael
  3. 3.Institut Montpelliérain Alexander GrothendieckUniversité de MontpellierMontpellier CedexFrance

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