On the intersection conjecture for infinite trees of matroids

TL;DR

This paper introduces a new technique to prove special cases of the matroid intersection conjecture, focusing on tame matroids with common 2-separation decompositions into finite parts.

Contribution

It establishes the conjecture for a broad class of tame matroids with shared 2-separation decompositions, advancing understanding of the intersection problem.

Findings

Proves the matroid intersection conjecture for certain tame matroids.

Develops a new technique applicable to infinite matroids.

Identifies conditions under which the conjecture holds for decomposed matroids.

Abstract

Using a new technique, we prove a rich family of special cases of the matroid intersection conjecture. Roughly, we prove the conjecture for pairs of tame matroids which have a common decomposition by 2-separations into finite parts.