On the intersections of circuits and cocircuits in matroids |
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Authors: | James G. Oxley |
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Affiliation: | (1) Mathematics Department, Louisiana State University, 70803 Baton Rouge, Louisiana, USA |
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Abstract: | Seymour has shown that a matroid has a triad, that is, a 3-element set which is the intersection of a circuit and a cocircuit, if and only if it is non-binary. In this paper we determine precisely when a matroidM has a quad, a 4-element set which is the intersection of a circuit and a cocircuit. We also show that this will occur ifM has a circuit and a cocircuit meeting in more than four elements. In addition, we prove that if a 3-connected matroid has a quad, then every pair of elements is in a quad. The corresponding result for triads was proved by Seymour. |
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Keywords: | 05 B 35 |
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