wovepaper · research, woven together

papers

Publications (73)

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.CO2021

Enumeration of extensions of the cycle matroid of a complete graph

Peter Nelson, Shayla Redlin, Jorn van der Pol

We prove that the number of single element extensions of $M (K_{n + 1})$ is $2^{(n /2 n) (1 + o (1))}$ . This is done using a characterization of extensions as "linear subclasses".

math.CO2025

Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified

Martin Dvorak, Tristan Figueroa-Reid, Rida Hamadani +8

Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory fa…

math.CO2012

A Density Hales-Jewett Theorem for matroids

Jim Geelen, Peter Nelson

We show that, if $I^\pm > 0$ is a real number, $n \geq 2$ and $ℓ \geq 2$ are integers, and $q$ is a prime power, then every simple matroid $M$ of sufficiently large rank, with no $U_{…

math.CO2018

Matroids with no $U_{2, n}$ -minor and many hyperplanes

Adam Brown, Peter Nelson

We construct, for every $r \geq 3$ and every prime power $q > 10$ , a rank- $r$ matroid with no $U_{2, q + 2}$ -minor, having more hyperplanes than the rank- $r$ projective geometry over $…

math.CO2012

An analogue of the ErdÅs-Stone theorem for finite geometries

Jim Geelen, Peter Nelson

For a set $G$ of points in $\PG(m-1,q)$, let $\ex_q(G;n)$, denote the maximum size of a collection of points in $\PG(n-1,q)$ not containing a copy of $G$ , up to projective equivale…

Publications (73)

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

Enumeration of extensions of the cycle matroid of a complete graph

Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified

A Density Hales-Jewett Theorem for matroids

Matroids with no U2,n​-minor and many hyperplanes

An analogue of the ErdÅs-Stone theorem for finite geometries

Matroids with no $U_{2, n}$ -minor and many hyperplanes

An analogue of the ErdÅs-Stone theorem for finite geometries