Jim Geelen

collaborators

3 papers

math.CO2026

OpenAI's proof of the Cycle Double Cover Theorem

Jim Geelen

The following notes are my attempt to clarify, to myself, the OpenAI proof of the Cycle Double Cover Conjecture. This write-up offers no new insights, but some people may find it e…

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…