Jim Geelen

most citedInequivalent Representations of Matroids over Prime Fields

4 citations · 6 across the 3 of their papers we have counts for

collaborators

3 papers

math.CO2011

The number of points in a matroid with no n-point line as a minor

Jim Geelen, Peter Nelson

For any positive integer $l$ we prove that if $M$ is a simple matroid with no $(l + 2)$ -point line as a minor and with sufficiently large rank, then $|E(M)|\le \frac{q^{r(M)}-1}{q-1}…

math.CO2011★ 2 cited

Certifying Non-representability of Matroids Over Prime Fields

Jim Geelen, Geoff Whittle

It is proved that, for a prime number $p$ , showing that an $n$ -element matroid is not representable over $GF (p)$ requires only $O (n^{2})$ rank evaluations.

math.CO2011★ 4 cited

Inequivalent Representations of Matroids over Prime Fields

Jim Geelen, Geoff Whittle

It is proved that for each prime field $GF (p)$ , there is an integer $f (p)$ such that a 4-connected matroid has at most $f (p)$ inequivalent representations over $GF (p)$ . We also pro…