It is known that a sequence of permutations is quasirandom if and only if the pattern density of every 4‐point permutation in converges to 1/24. We show that there is a set S of 4‐point permutations such that the sum of the pattern densities of the permutations from S in the permutations converges to if and only if the sequence is quasirandom. Moreover, we are able to completely characterize the sets S with this property. In particular, there are exactly ten such sets, the smallest of which has cardinality eight.

中文翻译：

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用模式和表征准随机排列

众所周知，当且仅当每4点置换的模式密度收敛到1/24时，置换序列才是准随机的。我们发现，有一组小号4点的排列使得从排列的图案密度的总和小号的排列收敛于 当且仅当该序列是准随机。此外，我们能够使用此属性完全表征集合S。特别地，恰好有十个这样的集合，其中最小的具有八位基数。