Lattice Path Matroid Polytopes

Abstract

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. 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.

arXiv admin note: text overlap with arXiv:math/0501246, arXiv:math/0211188, arXiv:0909.0840 by other authors

References in corpus (4)

• Lattice path matroids: enumerative aspects and Tutte polynomials
• Lattice Path Matroids: Structural Properties
• A quasisymmetric function for matroids
• Matroid base polytope decomposition

Cited by in corpus (3)

• Facial structures of lattice path matroid polytopes
• Eulerian-Catalan Numbers
• Toric $g$-polynomials of hook shape lattice Path Matroid Polytopes and product of simplices