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arXiv · 2510.11105

On Sibuya trees and forests

Thierry E Huillet
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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.

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Thierry E Huillet. 2025-10-13. On Sibuya trees and forests. https://arxiv.org/abs/2510.11105

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