论文标题
随机树或森林置换中的模式发生数量
The number of occurrences of patterns in a random tree or forest permutation
论文作者
论文摘要
树木排列和森林排列的类别由Acan和Hitczenko（2016）定义。我们研究了这些类别的给定长度的随机排列，尤其是在这些随机排列之一中固定模式的发生数量。主要结果表明，这些数字的分布在渐近上是正常的。 该证明使用随机树和森林排列的表示，使我们能够以$ u $统计量的类型表达模式的发生数。然后，我们为后者使用一般限制定理。
The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of these random permutations. The main results show that the distributions of these numbers are asymptotically normal. The proof uses representations of random tree and forest permutations that enable us to express the number of occurrences of a pattern by a type of $U$-statistics; we then use general limit theorems for the latter.
