Lattice Path Matroid Polytopes
نویسنده
چکیده
Fix two lattice paths P and Q from (0, 0) to (m, r) that use East and North steps with P never going above Q. Bonin et al. in [1] show that the lattice paths that go from (0, 0) to (m, r) and remain bounded by P and Q can be identified with the bases of a particular type of transversal matroid, which we call it a lattice path matroid. In this paper, we consider properties of lattice path matroid polytopes. These are the polytopes associated to the lattice path matroids. We investigate their face structure, decomposition, triangulation, Ehrhart polynomial and volume.
منابع مشابه
Euler Polytopes and Convex Matroid Optimization
Del Pia and Michini recently improved the upper bound of kd due to Kleinschmidt and Onn for the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. We introduce Euler polytopes which include a family of lattice polytopes with diameter (k + 1)d/2, and thus reduce the gap between the lower and upper bounds. In addition, we...
متن کاملLattice path matroids: The excluded minors
A lattice path matroid is a transversal matroid for which some antichain of intervals in some linear order on the ground set is a presentation. We characterize the minor-closed class of lattice path matroids by its excluded minors.
متن کامل1 1 N ov 2 00 4 MATROID POLYTOPES , NESTED SETS AND BERGMAN FANS
The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid polytopes, we present a geometric construction of the Bergman fan, and we discuss its relationship with the simplicial complex of nested sets in the lattice of flats. The Bergman complex is triangulated by the nested se...
متن کاملO / 0 41 12 60 v 1 1 1 N ov 2 00 4 MATROID POLYTOPES , NESTED SETS AND BERGMAN FANS
The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid polytopes, we present a geometric construction of the Bergman fan, and we discuss its relationship with the simplicial complex of nested sets in the lattice of flats. The Bergman complex is triangulated by the nested se...
متن کاملLattice Subdivisions and Tropical Oriented Matroids Featuring ∆ N−1 × ∆ D−1
Lattice Subdivisions and Tropical Oriented Matroids Featuring ∆ n−1 × ∆ d−1 LindsayCPiechnik Subdivisions of products of simplices, and their applications, appear across mathematics. In this thesis, they are the tie between two branches of my research: polytopal lattice subdivisions and tropical oriented matroid theory. The first chapter describes desirable combinatorial properties of subdivisi...
متن کامل