A minor-closed class of matroids is (strongly) fractal if the number of n-element matroids in the class is dominated by the number of n-element excluded minors. We conjecture that when K is an infinite field, the class of K-representable matroids is strongly fractal. We prove that the class of sparse paving matroids with at most k circuit-hyperplanes is a strongly fractal class when k is at least three. The minor-closure of the class of spikes with at most k circuit-hyperplanes (with k>4) satisfies a strictly weaker condition: the number of 2t-element matroids in the class is dominated by the number of 2t-element excluded minors. However, there are only finitely many excluded minors with ground sets of odd size.

中文翻译：

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拟阵的分形类

如果类中的 n 元素拟阵的数量由 n 元素排除的次要的数量主导，则该类的次要封闭拟阵是（强）分形的。我们推测，当 K 是一个无限域时，K 可表示拟阵类是强分形的。我们证明，当 k 至少为 3 时，具有至多 k 个电路超平面的稀疏铺砌拟阵类是强分形类。具有至多 k 个电路超平面（k>4）的尖峰类的次要闭合满足严格较弱的条件：类中 2t 元素拟阵的数量由 2t 元素排除的次要数量主导。然而，只有有限数量的被排除的未成年人具有奇数大小的地面集。