A construction of infinite sets of intertwines for pairs of matroids

TL;DR

This paper constructs infinite families of intertwines for certain pairs of matroids, expanding understanding of their structure and properties in matroid theory.

Contribution

It introduces a method to construct infinite sets of intertwines for pairs of matroids under specific conditions, a novel contribution to matroid theory.

Findings

Constructed infinite sets of intertwines for pairs of matroids.

Analyzed properties of the constructed intertwines.

Extended the theory of matroid minors and extensions.

Abstract

An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair. For pairs for which neither matroid can be obtained, up to isomorphism, from the other by taking free extensions, free coextensions, and minors, we construct a family of rank-k intertwines for each sufficiently large integer k. We also treat some properties of these intertwines.