Inequivalent representations of ternary matroids

Abstract

This paper considers representations of ternary matroids over fields other than GF(3). It is shown that a 3-connected ternary matroid representable over a finite field F has at most $\text{¦F¦ - 2}$ inequivalent representations over F. This resolves a special case of a conjecture of Kahn in the affirmative.