A fringe subtree of a rooted tree is a subtree induced by one of the vertices and all its descendants. We consider the problem of estimating the number of distinct fringe subtrees in two types of random trees: simply generated trees and families of increasing trees (recursive trees, $d$-ary increasing trees and generalized plane-oriented recursive trees). We prove that the order of magnitude of the number of distinct fringe subtrees (under rather mild assumptions on what `distinct' means) in random trees with $n$ vertices is $n/\sqrt{\log n}$ for simply generated trees and $n/\log n$ for increasing trees.

翻译：根树的边缘亚树枝是由一个脊椎及其后代引生的子树。我们考虑了估计两类随机树中不同的边缘亚树数量的问题:仅生树和树木增加的家族(树再生、以美元计增长的树木和以平面为方向的普通循环树)。我们证明,在胡乱树木中,具有“明显”含义的“模糊”一词假设值相当温和的细树数量的数量,对于仅生树来说是$/\sqrt\log n},对于增加树木而言是$/sqrt\log n$/n/log n$。