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arXiv · 2003.06450

On bucket increasing trees, clustered increasing trees and increasing diamonds

Markus Kuba·Alois Panholzer
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Abstract

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.

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Markus Kuba, Alois Panholzer. 2020-03-13. On bucket increasing trees, clustered increasing trees and increasing diamonds. https://arxiv.org/abs/2003.06450

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