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.

12 pages. This revised version includes revisions suggested by referees. The paper will appear in JCTb