A note on hook length formulas for trees

TL;DR

This paper discusses recent developments in hook length formulas for trees, unifying previous results and exploring formulas related to families of increasingly labeled trees.

Contribution

It provides a unified view of hook length formulas and introduces natural formulas for specific families of labeled trees.

Findings

Unifies various existing hook length formulas.

Introduces natural hook length formulas for labeled trees.

Clarifies the combinatorial significance of these formulas.

Abstract

In this short note we discuss recent results on hook length formulas of trees unifying some earlier results, and explain hook length formulas naturally associated to families of increasingly labelled trees.