On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial

Kolja Knauer, Leonardo Martínez-Sandoval, Jorge Luis Ramírez Alfonsín

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

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.

Original languageEnglish
Pages (from-to)698-719
Number of pages22
JournalDiscrete and Computational Geometry
Volume60
Issue number3
DOIs
StatePublished - 1 Oct 2018

Keywords

  • Distributive polytope
  • Ehrhart polynomial
  • Lattice path matroid
  • Matroid base polytope

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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