Work

The Genesis Sequence, Tree Records and Endofunctions

Year: 2026

Type: article

Abstract: We present bijections connecting tree records, the girth of a connected endofunction, and the genesis sequence (the first sequence in OEIS). Using these, we derive generating functions for tree and forest record numbers in terms of Cayley's tree function and give a new proof of Cayley's forest formula.

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.445.11

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

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: European Commission, Natural Sciences and Engineering Research Council of Canada, Agencia Estatal de Investigación

Awards: G3480869486, G4442677895, G4526231891, G7084143925

OpenAlex ID: W7163745860

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