On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial

被引：0
|
作者：
Kolja Knauer
Leonardo Martínez-Sandoval
Jorge Luis Ramírez Alfonsín
机构：
[1] Aix-Marseille Université and CNRS,Laboratoire d’Informatique Fondamentale, Faculté des Sciences de Luminy
[2] Ben-Gurion University of the Negev,Department of Computer Science, Faculty of Natural Sciences
[3] Université de Montpellier,Institut Montpelliérain Alexander Grothendieck
来源：
Discrete & Computational Geometry | 2018年 / 60卷
关键词：
Ehrhart polynomial; Distributive polytope; Matroid base polytope; Lattice path matroid;
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学科分类号：
摘要：
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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页码：698 / 719
页数：21
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