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math.CO2025
On the enumeration of records of rooted trees and rooted forests
Adrián Lillo, Mercedes Rosas, Stefan Trandafir
A record of a rooted Cayley tree is a node whose label is the largest along the unique path to the root. In this work, we find elegant functional equations relating the generating…
math.CO2025
On Weary Drivers, Records of Trees, and Parking Functions
Adrián Lillo, Mercedes Rosas, Stefan Trandafir
This work builds on the notion of record of rooted trees. We provide an alternative definition of parking functions, derive from it a record-preserving bijection between rooted tre…