Two kinds of hook length formulas for complete $m$-ary trees

TL;DR

This paper introduces two types of hook length formulas for internal vertices of complete m-ary trees, extending previous results and providing new combinatorial identities.

Contribution

It defines two new hook length concepts for complete m-ary trees and derives their formulas, generalizing earlier work by Du and Liu.

Findings

Derived two new hook length formulas for m-ary trees

Generalized previous hook length results

Enhanced understanding of combinatorial properties of m-ary trees

Abstract

In this paper, we define two kinds of hook length for internal vertices of complete $m$-ary trees, and deduce their corresponding hook length formulas, which generalize the main results obtained by Du and Liu.