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A result of Walton and the author establishes that every 3-connected matroid of rank and corank at least three has one of five 6-element rank-3 self-dual matroids as a minor. One of these matroids is the rank-3 whirl W3. Another is the rank-3 matroid P6 that consists of a single 3-point line together with three points off the line. This paper determines the structure of the class of matroids that is obtained by excluding as minors both W3 and P6. As a consequence of this result, we deduce a characterization of the class of GF(4)-representable matroids with no W3-minor. © 1990.

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Discrete Mathematics

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