Orienting matroids representable over both GF(3) and GF(5)
type: Item
instance of: scholarly article
title: Orienting matroids representable over both GF(3) and GF(5)
zbMATH Open document ID: 0937.05029
author: Jon Lee
published in: European Journal of Combinatorics
publication date: 2000-06-04T00:00:00Z
review text: The paper provides a simple, constructive proof of the fact that matroids that are representable over both GF(3) and GF(5) are also orientable. The proof relies on a result proved by the author in [J. Comb. Theory, Ser. B. 50, No. 2, 265-287 (1990; Zbl 0657.05017)]. In the course of the proof, a special \(D_0^8\)-mapping for \(\mathcal M\) is constructed, where \(D_0^8=\{0, \pm 1, \pm 2, \pm 4, \pm 8\}\). For such a mapping, there is a naturally arising \(\Sigma\)-mapping for \(\mathcal M\) into \(\Sigma=\{-, 0, +\}\). This \(\Sigma\)-mapping is derived from the \(D_0^8\)-mapping, and it is checked against the necessary conditions for orientability. The paper is concluded with a number of examples.
reviewed by: Ferenc Fodor
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 52C40
zbMATH DE Number: 1417659
zbMATH Keywords: matroid representations
zbMATH Keywords: orientable matroid
MaRDI profile type: Publication
full work available at URL: eujc.1999.0308
OpenAlex ID: W2090580978
cites work: Q4003411
cites work: The incidence structure of subspaces with well-scaled frames
cites work: A characterization of the orientations of ternary matroids
cites work: Q3135082
cites work: On Matroids Representable over 𝐺𝐹(3) and Other Fields
cites work: A characterisation of the matroids representable over GF(3) and the rationals
DOI: 10.1006/EUJC.1999.0308
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description: scientific article; zbMATH DE number 1417659