The genesis sequence, tree records and endofunctions

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Enrica Duchi, Adrián Lillo, Pablo Puerto, Mercedes Rosas, Stefan Trandafir
Cited by: 0

Abstract

In this work, we present a series of bijections that reveal the deep connections between the concepts of tree records, the girth of a connected endofunction, and the genesis sequence, the first sequence in the OEIS. We use these results to derive the generating functions for the tree and forest record numbers, expressing them in terms of the Cayley's tree function. Finally, we provide a new proof for Cayley's forest formula.

Fields of Study & Subjects

Advanced Combinatorial Mathematics Advanced Mathematical Identities Graph theory and applications

Publication details

Journal / source
arXiv (Cornell University)
Publication date
12 January 2026
Document type
Preprint