New hook length formulas for binary trees

TL;DR

This paper introduces two novel hook length formulas for binary trees where the hook length appears as an exponent, offering new combinatorial identities.

Contribution

The paper presents two new hook length formulas for binary trees with the hook length appearing as an exponent, a novel combinatorial approach.

Findings

Two new hook length formulas involving exponents

Formulas apply specifically to binary trees

Provides new combinatorial identities

Abstract

We find two new hook length formulas for binary trees. The particularity of our formulas is that the hook length $h_v$ appears as an exponent.