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Abstract : |
It follows from a fundamental (1958) result of Tutte that a binary matroid is representable over the rationals if and only if it can be represented by a totally unimodular matrix, that is, by a matrix over the rationals with the property that all subdeterminants belong to f0; 1; 1g. For an arbitrary eld F, it is of interest to ask for a matrix characterisation of those matroids representable over F and the rationals. In this paper this question is answered when F is GF (3). It is shown that a ternary matroid is representable over the rationals if and only if it can be represented over the rationals by a matrix A with the property that all subdeterminants of A belong to the set f0; 2 i, |
