On lattice path matroid polytopes: integer points and Ehrhart polynomial

2017/01/19 by Kolja Knauer, Knauer, Kolja, Leonardo Martínez-Sandoval +3 · 3 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1701.05529

openalex publication_date 2017/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Chow classes of matroids and standard Young tableaux
• Positroidal aspects of non-nesting rook placements
• Hamiltonian connectivity of some base-cobase graphs

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