Representation of matroids with a modular plane
Combinatorics
2013-04-25 v1
Abstract
We prove that if M is a vertically 4-connected matroid with a modular flat X of rank at least three, then every representation of M | X over a finite field F extends to a unique F-representation of M. A corollary is that when F has order q, any vertically 4-connected matroid with a PG(2, F)-restriction is either F-representable or has a U_{2, q^2+1}-minor. We also show that no excluded minor for the class of F-representable matroids has a PG(2, F)-restriction.
Cite
@article{arxiv.1304.6448,
title = {Representation of matroids with a modular plane},
author = {Jim Geelen and Rohan Kapadia},
journal= {arXiv preprint arXiv:1304.6448},
year = {2013}
}
Comments
59 pages. Submitted