  This paper studies structural aspects of lattice path matroids, a class of
transversal matroids that is closed under taking minors and duals. Among the
basic topics treated are direct sums, duals, minors, circuits, and connected
flats. One of the main results is a characterization of lattice path matroids
in terms of fundamental flats, which are special connected flats from which one
can recover the paths that define the matroid. We examine some aspects related
to key topics in the literature of transversal matroids and we determine the
connectivity of lattice path matroids. We also introduce notch matroids, a
minor-closed, dual-closed subclass of lattice path matroids, and we find their
excluded minors.

Combinatorics