Work

On lattice path matroid polytopes: integer points and Ehrhart polynomial

Year: 2017

Type: preprint

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.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

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

Institutions: Centre National de la Recherche Scientifique, Aix-Marseille Université, Laboratoire d’Informatique Fondamentale de Marseille, Ben-Gurion University of the Negev, Université de Montpellier, Institut Montpelliérain Alexander Grothendieck

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2951472640

Cites: 16

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Related to: 10