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In the mathematical theory of matroids, a paving matroid is a matroid in which every circuit has size at least as large as the matroid's rank. In a matroid of rank r {\displaystyle r} every circuit has size at most r + 1 {\displaystyle r+1} , so it is equivalent to define paving matroids as the matroids in which the size of every circuit belongs to the set { r , r + 1 } {\displaystyle \{r,r+1\}}. It has been conjectured that almost all matroids are paving matroids.
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