On Sibuya trees and forests
Combinatorics
2025-10-14 v1 Probability
Abstract
We show that the Sibuya distribution and its non-critical relatives are relevant in the context of the recursive generation of both simply generated and increasing critical trees' and forests' progenies. A special class of generalized Stirling numbers are at the heart of the analysis of the induced occupancy distributions. Asymptotic aspects of large forests are addressed.
Keywords
Cite
@article{arxiv.2510.11105,
title = {On Sibuya trees and forests},
author = {Thierry E Huillet},
journal= {arXiv preprint arXiv:2510.11105},
year = {2025}
}