On Weak Maps of Ternary Matroids

Abstract

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.

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