论文标题
在桶增加树木上，簇生的树木簇生和增加钻石
On bucket increasing trees, clustered increasing trees and increasing diamonds
论文作者
论文摘要
在这项工作中，我们分析了增加树木家庭的桶。我们介绍了两个简单的随机增长过程，生成随机的桶增加尺寸$ n $的树木，并补充了Mahmoud和Smythe的早期结果，用于桶形递归树。在组合方面，我们定义了树族的多鉴定概括，$ d $ d $ ARY增加了树木和普遍面向飞机的递归树。此外，我们引入了一个聚类过程，用于普通的增加树木，并将其与增加树木的水桶相关联。我们详细讨论了桶尺寸的二大，并在此类桶增加的树族家族与某些称为增加钻石的图形家族之间进行了两次培养，从而为Bodini等人观察到的现象提供了解释。
In this work we analyze bucket increasing tree families. We introduce two simple stochastic growth processes, generating random bucket increasing trees of size $n$, complementing the earlier result of Mahmoud and Smythe for bucket recursive trees. On the combinatorial side, we define multilabelled generalizations of the tree families $d$-ary increasing trees and generalized plane-oriented recursive trees. Additionally, we introduce a clustering process for ordinary increasing trees and relate it to bucket increasing trees. We discuss in detail the bucket size two and present a bijection between such bucket increasing tree families and certain families of graphs called increasing diamonds, providing an explanation for phenomena observed by Bodini et al.
