A Unifying Approach for Proving Hook-Length Formulas for Weighted Tree Families

We propose an expansion technique for weighted tree families, which unifies and extends recent results on hook-length formulas of trees obtained by Han [10], Chen et al. [3], and Yang [19]. Moreover, the approach presented is used to derive new hook-length formulas for tree families, where several hook-functions in the corresponding expansion formulas occur in a natural way. Furthermore we consider families of increasingly labelled trees and show close relations between hook-length formulas for such tree families and corresponding ones for weighted tree families.