On the matroids representable over \(GF(4)\)
type: Item
instance of: scholarly article
title: On the matroids representable over \(GF(4)\)
zbMATH Open document ID: 0568.05014
DOI: 10.1016/0095-8956(86)90049-3
author: James Oxley
published in: Journal of Combinatorial Theory. Series B
publication date: 1986-01-01T00:00:00Z
review text: One of the fundamental problems in matroid theory is the determination of the excluded minors for representability over the fields \(GF(q)\). This problem has only been solved when \(q\) is 2 or 3. This note considers this problem for \(q=4\). In particular, it is proved that a certain eight- element self-dual matroid is minor-minimal with the property of being nonrepresentable over \(GF(4)\). This matroid provides a counterexample to a conjecture of Kahn and Seymour that the excluded minors in this case consist of the six-point line and its dual, the non-Fano matroid and its dual, and one other six-element self-dual matroid.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 3906509
zbMATH Keywords: representable matroids
zbMATH Keywords: excluded minors
MaRDI profile type: Publication
full work available at URL: 0095-8956(86)90049-3
OpenAlex ID: W2064767396
cites work: Q4173891
cites work: THE CRITICAL PROBLEM FOR POLYMATROIDS
description: scientific article; zbMATH DE number 3906509