Discrete CATS Seminar
U N I V E R S I T Y
K E N T U C K Y
WHERE CATS =
845 PATTERSON OFFICE TOWER
2011 - 2012
"Lattice path matroid polytopes"
MIT and North Carolina State University
Monday, April 16, 2012
845 Patterson Office Tower
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 a lattice path matroid.
In this paper, we consider properties of the 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. We also briefly look
over Ehrhart polynomial of alcoved polytopes as well as the
Eulerian-Catalan numbers which are closely related.