Matthew E. Kroeker

activity

20172026

most citedOn the Mean Order of Connected Induced Subgraphs of Block Graphs

10 citations · 18 across the 7 of their papers we have counts for

collaborators

10 papers

math.CO2026

Unavoidable flats in GF(q)-representable matroids

Jim Geelen, Matthew E. Kroeker, Peter Nelson

We show that, for any finite field $F$ and positive integer $k$ , a simple $F$ -representable matroid $M$ with sufficiently high rank contains a rank- $k$ flat which…

math.CO2026

Ordinary lines, point degrees, and matroid density

Matthew E. Kroeker, Ben Lund

For every set of $n$ points in $C^{d}$ with full affine span, we prove that some point lies on at least $n + 1 - 2 n / (d + 1)$ spanned lines, which is best possible in every dimensi…

math.CO2025

Rainbow triangles and the Erdős-Hajnal problem in projective geometries

Carolyn Chun, James Dylan Douthitt, Wayne Ge +3

We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs, in both its usual 'induced' form and the multicolou…

math.CO2024

Characterizing real-representable matroids with large average hyperplane-size

Rutger Campbell, Matthew E. Kroeker, Ben Lund

Generalizing a theorem of the first two authors and Geelen for planes, we show that, for a real-representable matroid $M$ , either the average hyperplane-size in $M$ is at most a co…

math.CO2023

Average plane-size in complex-representable matroids

Rutger Campbell, Jim Geelen, Matthew E. Kroeker

Melchior's inequality implies that the average line-length in a simple, rank- $3$ , real-representable matroid is less than $3$ . A similar result holds for complex-representable matr…

math.CO2023

Unavoidable flats in matroids representable over prime fields

Jim Geelen, Matthew E. Kroeker

We show that, for any prime $p$ and integer $k \geq 2$ , a simple GF( $p$ )-representable matroid with sufficiently high rank has a rank- $k$ flat which is either independent in $M$ , o…