On the enumeration of records of rooted trees and rooted forests

Adrián Lillo; Mercedes Rosas; Stefan Trandafir

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arXiv · 2510.12536

On the enumeration of records of rooted trees and rooted forests

Adrián Lillo·Mercedes Rosas·Stefan Trandafir

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Abstract

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 functions for records of rooted Cayley trees and for records of forests of rooted trees with the Cayley tree function, and explore the consequences of our results.

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Adrián Lillo, Mercedes Rosas, Stefan Trandafir. 2025-10-14. On the enumeration of records of rooted trees and rooted forests. https://arxiv.org/abs/2510.12536

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