On Weak Maps of Ternary Matroids
Let M and N be ternary matroids having the same rank and the same
ground set, and assume that every independent set in N is also
independent in M. The main result of this paper proves that if $M$ is
3-connected and N is connected and non-binary, then M = N.
A related result characterizes precisely when a matroid that is obtained by
relaxing a circuit-hyperplane of a ternary matroid is also ternary.