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cs.DM2026
The Genesis Sequence, Tree Records and Endofunctions
Enrica Duchi, Adrián Lillo, Pablo Puerto +2
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 funct…
math.CO2026
The Priority Lattice
Adrián Lillo, Mercedes Rosas
We introduce the priority lattice, a structure arising from the priority search algorithm on rooted trees and forests. We prove bijectively that its maximal chains are labeled by p…
math.CO2026
The genesis sequence, tree records and endofunctions
Enrica Duchi, Adrián Lillo, Pablo Puerto +2
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 sequen…