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On Inequivalent Representations of Matroids over Finite Fields

✍ Scribed by James Oxley; Dirk Vertigan; Geoff Whittle

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 586 KB
Volume: 67
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1996.0049

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✦ Synopsis

Kahn conjectured in 1988 that, for each prime power q, there is an integer n(q) such that no 3-connected GF(q)-representable matroid has more than n(q) inequivalent GF(q)-representations. At the time, this conjecture was known to be true for q=2 and q=3, and Kahn had just proved it for q=4. In this paper, we prove the conjecture for q=5, showing that 6 is a sharp value for n(5). Moreover, we also show that the conjecture is false for all larger values of q.

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