We consider permutations avoiding a pattern of length three under the family of Mallows distributions. In particular, for any pattern , we obtain rather precise results on the asymptotic probability as n → ∞ that a permutation under the Mallows distribution with parameter q ∈ (0, 1) avoids the pattern. By a duality between the parameters q and , we also obtain rather precise results on the above probability for q > 1 and any pattern .

中文翻译：

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避免在Mallows分布下使用长度为3的模式的排列

我们考虑在Mallows分布族下避免使用长度为3的模式的置换。特别地，对于任何模式，我们获得的渐近概率相当精确的结果Ñ  →交通 ∞一个置换与参数的锦葵分布下q  ∈（0，1）避免了图案。通过参数q和的对偶性，我们还获得了q  > 1和任何模式的上述概率的相当精确的结果。