The Genesis Sequence, Tree Records and Endofunctions
Copyright policy )The Genesis Sequence, Tree Records and Endofunctions
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.
In Proceedings GASCom 2026, arXiv:2606.09910. This is an extended abstract of arXiv:2601.07938. This work is dedicated to Neil J. A. Sloane, renowned number-crusher, for his creation and tireless curation of the Online Encyclopedia of Integer Sequences
05A19 (Primary) 05A15 (Secondary), FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Combinatorics, Discrete Mathematics, FOS: Mathematics, Combinatorics (math.CO), G.2.1, G.2.2
05A19 (Primary) 05A15 (Secondary), FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Combinatorics, Discrete Mathematics, FOS: Mathematics, Combinatorics (math.CO), G.2.1, G.2.2
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