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{{IncludeOpenProblem|Equitability of matroids}}
The above sequence of exchanges shows that there is a linear order of the elements where any interval of length ''r'' is a basis. This does not imply smoothnessequitability, but if there would be a ''cyclic'' order with this property then smoothness equitability would follow. The conjecture on [[Cyclic orderings of matroids]] states that such a cyclic order always exists:
{{IncludeOpenProblem|Cyclic orderings of matroids}}
