On inequivalent representations of matroids over finite fields
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
Oxley, J., Vertigan, D., & Whittle, G. (1996). On inequivalent representations of matroids over finite fields. Journal of Combinatorial Theory. Series B, 67 (2), 325-343. https://doi.org/10.1006/jctb.1996.0049