Year: 2013
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Geelen, Jim, Kapadia, Rohan
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1556020987