Generate $\Delta$-matroids from matroids

TL;DR

This paper characterizes when two matroids on the same set can form the upper and lower matroids of a $ abla$-matroid, providing a complete set of conditions for their relationship.

Contribution

It establishes necessary and sufficient conditions for two matroids to be the upper and lower matroids of a $ abla$-matroid, advancing the understanding of $ abla$-matroid structure.

Findings

Provides a complete characterization of matroid pairs forming a $ abla$-matroid

Identifies key conditions for the existence of $ abla$-matroids from given matroids

Enhances the theoretical framework connecting matroids and $ abla$-matroids

Abstract

We give necessary and sufficient conditions for two matroids on the same ground set to be the upper and lower matroid of a $\Delta$-matroid.