Work

The genesis sequence, tree records and endofunctions

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2601.07938

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

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7124188812

Cites:

Cited by:

Related to: