P. Nelson

activity

20112026

most citedAlmost all matroids are non-representable

18 citations · 38 across the 33 of their papers we have counts for

collaborators

Showing 2014Show all

7 papers · 1 filter

math.CO2014

The densest matroids in minor-closed classes with exponential growth rate

Jim Geelen, Peter Nelson

The $growth rate function$ for a nonempty minor-closed class of matroids $M$ is the function $h_{M} (n)$ whose value at an integer $n \geq 0$ is define…

math.CO2014

Matroids denser than a projective geometry

Peter Nelson

The growth-rate function for a minor-closed class $M$ of matroids is the function $h$ where, for each non-negative integer $r$ , $h (r)$ is the maximum number of elements o…

math.CO2014

Matroids denser than a clique

Jim Geelen, Peter Nelson

The growth-rate function for a minor-closed class $M$ of matroids is the function $h$ where, for each non-negative integer $r$ , $h (r)$ is the maximum number of elements o…

math.CO2014★ 3 cited

The critical number of dense triangle-free binary matroids

Jim Geelen, Peter Nelson

We show that, for each real number $ε > 0$ there is an integer $c$ such that, if $M$ is a simple triangle-free binary matroid with $∣ M ∣ \geq (\frac{1}{4} + ε) 2^{r (M)}$ , then $M$ ha…

math.CO2014

On the existence of asymptotically good linear codes in minor-closed classes

Peter Nelson, Stefan H. M. van Zwam

Let $C = (C_{1}, C_{2}, \dots)$ be a sequence of codes such that each $C_{i}$ is a linear $[n_{i}, k_{i}, d_{i}]$ -code over some fixed finite field $F$ , where $n_{i}$ is the le…

math.CO2014★ 2 cited

Odd circuits in dense binary matroids

Jim Geelen, Peter Nelson

We show that, for each real number $α > 0$ and odd integer $k \geq 5$ there is an integer $c$ such that, if $M$ is a simple binary matroid with $∣ M ∣ \geq α 2^{r (M)}$ and with no $k$ -ele…