14 citations · 31 across the 21 of their papers we have counts for
4 papers · 1 filter
On minor-closed classes of matroids with exponential growth rate
Jim Geelen, Peter Nelson
Let $\cM$ be a minor-closed class of matroids that does not contain arbitrarily long lines. The growth rate function, $h:\bN\rightarrow \bN$ of $\cM$ is given by $$h(n) = \max(|M|\…
Matroid 3-connectivity and branch width
Jim Geelen, Stefan H. M. van Zwam
We prove that, for each nonnegative integer k and each matroid N, if M is a 3-connected matroid containing N as a minor, and the the branch width of M is sufficiently large, then t…
Certifying Non-representability of Matroids Over Prime Fields
Jim Geelen, Geoff Whittle
It is proved that, for a prime number , showing that an -element matroid is not representable over requires only rank evaluations.
Inequivalent Representations of Matroids over Prime Fields
Jim Geelen, Geoff Whittle
It is proved that for each prime field , there is an integer such that a 4-connected matroid has at most inequivalent representations over . We also pro…