Taking minors without splitting tangles

TL;DR

This paper proves that in any matroid, elements can be removed via deletion or contraction without disrupting the structure of any existing tangle, ensuring the integrity of the tangle is maintained.

Contribution

It introduces a method to remove elements from a matroid without splitting any tangles, a novel approach in matroid theory.

Findings

Any element in a matroid can be removed without splitting tangles.

The method preserves the structure of all tangles during element removal.

This result advances understanding of matroid decompositions.

Abstract

We prove that any element in a matroid can be removed, by either deletion or contraction, in such a way that no tangle "splits".