Title

On inequivalent representations of matroids over finite fields

Document Type

Article

Publication Date

1-1-1996

Abstract

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. © 1996 Academic Press, Inc.

Publication Source (Journal or Book title)

Journal of Combinatorial Theory. Series B

First Page

325

Last Page

343

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