On Rota's Conjecture and nested separations in matroids

Abstract

We prove that for each finite field $\mathbb F$ and integer $k\in \mathbb Z$ there exists $n\in \mathbb Z$ such that no excluded minor for the class of $\mathbb F$-representable matroids has $n$ nested $k$-separations.Comment: 12 pages. This revised version includes revisions suggested by referees. The paper will appear in JCT