Statistical Aspects of Two Classes of Random Binomial Trees and Forests

Thierry E. Huillet ()
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Thierry E. Huillet: Laboratoire de Physique Théorique et Modélisation (CNRS, UMR 8089), CY Cergy Paris Université, 95302 Cergy-Pontoise, France

Mathematics, 2025, vol. 13, issue 2, 1-31

Abstract: We consider two specific families of binomial trees and forests: simply generated binomial d -ary trees and forests versus their increasing phylogenetic version, with tree nodes in increasing order from the root to any of its leaves. The analysis (both pre-asymptotic and asymptotic) consists of some of the main statistical features of their total progenies. We take advantage of the fact that the random distribution of those trees are obtained while weighting the counts of the underlying combinatorial trees. We finally briefly stress a rich alternative randomization of combinatorial trees and forests, based on the ratio of favorable count outcomes to the total number of possible ones.

Keywords: simply generated and increasing binomial trees and forests; total progeny; generating functions; Lagrange inversion formula; structural statistics; partition structures; combinatorial probability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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