On bucket increasing trees, clustered increasing trees and increasing diamonds

Abstract In this work we analyse bucket increasing tree families. We introduce two simple stochastic growth processes, generating random trees of size n , complementing the earlier result Mahmoud and Smythe (1995, Theoret. Comput. Sci. 144 221–249.) for recursive trees. On combinatorial side, define multilabelled generalisations families d -ary generalised plane-oriented Additionally, a clustering process ordinary relate it to discuss in detail present bijection between such certain graphs called diamonds, providing an explanation phenomena observed by Bodini et al. (2016, Lect. Notes 9644 207–219.). Concerning structural properties trees, parameter $K_n$ . It counts initial node containing label is closely related distribution types. parameters descendants j degree distributional decompositions, extending results (Kuba Panholzer (2010), 411 (34–36) 3255–3273.).