Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4656800 | Journal of Combinatorial Theory, Series B | 2015 | 8 Pages |
Abstract
We prove that, for each prime power q, there is an integer n such that if M is a 3-connected, representable matroid with a PG(n−1,q)PG(n−1,q)-minor and no U2,q2+1U2,q2+1-minor, then M is representable over GF(q)GF(q). We also show that for ℓ≥2ℓ≥2, if M is a 3-connected, representable matroid of sufficiently high rank with no U2,ℓ+2U2,ℓ+2-minor and |E(M)|≥2ℓr(M)/2|E(M)|≥2ℓr(M)/2, then M is representable over a field of order at most ℓ.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jim Geelen, Rohan Kapadia,