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 language | English |
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Pages (from-to) | 698-719 |
Number of pages | 22 |
Journal | Discrete and Computational Geometry |
Volume | 60 |
Issue number | 3 |
DOIs | |
State | Published - 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