# One-adhesive polymatroids

## TL;DR

This paper investigates the properties of one-adhesive polymatroids, characterizing when two polymatroids can be glued together, with implications for entropy functions and extensions on five-element sets.

## Contribution

It provides a characterization of one-adhesive polymatroids and describes conditions for their extensions, advancing understanding of adhesive properties in polymatroid theory.

## Key findings

- Two polymatroids are one-adhesive if and only if related polymatroids have any extension.
- Characterization of adhesive polymatroid pairs on five-element sets.
- Connection between adhesive polymatroids and entropy functions.

## Abstract

Adhesive polymatroids were defined by F. Mat\'u\v{s} motivated by entropy functions. Two polymatroids are adhesive if they can be glued together along their joint part in a modular way; and are one-adhesive, if one of them has a single point outside their intersection. It is shown that two polymatroids are one-adhesive if and only if two closely related polymatroids have any extension. Using this result, adhesive polymatroid pairs on a five-element set are characterized.