Sticky polymatroids on at most five elements

TL;DR

This paper proves the sticky polymatroid conjecture for all polymatroids with at most five elements, confirming the conjecture in this specific case.

Contribution

It establishes the validity of the sticky polymatroid conjecture for small polymatroids with up to five elements, a previously unresolved case.

Findings

The conjecture holds for polymatroids on five or fewer elements.

Characterization of when extensions of polymatroids have an amalgam.

Confirmation of the conjecture's validity in small cases.

Abstract

The sticky polymatroid conjecture states that any two extensions of the polymatroid have an amalgam if and only if the polymatroid has no non-modular pairs of flats. We show that the conjecture holds for polymatroids on five or less elements.