The excluded minors for lattice path polymatroids

TL;DR

This paper identifies the excluded minors for the class of lattice path polymatroids, revealing their structure within Boolean polymatroids and showing they form a small, describable set despite being infinite.

Contribution

It characterizes the excluded minors for lattice path polymatroids, a new understanding within the broader context of polymatroid minor theory.

Findings

Excluded minors for lattice path polymatroids are classified into a small number of types.

The class of lattice path polymatroids is minor-closed and contained within Boolean polymatroids.

There are infinitely many excluded minors, but they are structurally well-understood.

Abstract

We find the excluded minors for the minor-closed class of lattice path polymatroids as a subclass of the minor-closed class of Boolean polymatroids. Like lattice path matroids and Boolean polymatroids, there are infinitely many excluded minors, but they fall into a small number of easily-described types.