Matroids in which every pair of elements belongs to both a 4-circuit and a 4-cocircuit

In this thesis, we analyse the matroids which have the property that every pair of elements belongs to both a 4-circuit and a 4-cocircuit. In particular, we show that if a matroid with this property has at least 13 elements, then it is a spike. We also study the matroids with fewer than 13 element that have this property.

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