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On the Excluded Minors for Quaternary Matroids

✍ Scribed by J.F. Geelen; J.G. Oxley; D.L. Vertigan; G.P. Whittle

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
221 KB
Volume
80
Category
Article
ISSN
0095-8956

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✦ Synopsis

This paper strengthens the excluded-minor characterization of GF(4)-representable matroids. In particular, it is shown that there are only finitely many 3-connected matroids that are not GF(4)-representable and that have no U 2, 6 -, U 4, 6 -, P 6 -, F & 7 -, or (F & 7 )*-minors. Explicitly, these matroids are all minors of S(5, 6, 12) with rank and corank at least 4, and P" 8 , the matroid that can be obtained from S(5, 6, 12) by deleting two elements, contracting two elements, and then relaxing the only pair of disjoint circuit-hyperplanes.

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