Lattice path matroids: the excluded minors

TL;DR

This paper characterizes the class of lattice path matroids by identifying the minimal matroids that are not in this class, providing a clear structural understanding of these matroids.

Contribution

It introduces a characterization of lattice path matroids through their excluded minors, advancing the structural theory of these matroids.

Findings

Identified the excluded minors for lattice path matroids.

Provided a complete characterization of the minor-closed class.

Enhanced understanding of the structural properties of lattice path matroids.

Abstract

A lattice path matroid is a transversal matroid for which some collection of incomparable 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.