The Genesis Sequence, Tree Records and Endofunctions

Published 12 Jun 2026 in cs.DM | (2606.14393v1)

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.

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