Hook Length Formulas for Trees by Han's Expansion
William Y. C. Chen, Oliver X.Q. Gao and Peter L. Guo
Abstract: Recently Han obtained a general formula for the weight function corresponding to the expansion of a series in terms of hook lengths of binary trees. In this paper, we present weight function formulas for k-ary trees, plane trees, plane forests, labeled trees and forests. We also find appropriate generating functions which lead to unifications of the hook length formulas due to Du and Liu, Han, Gessel and Seo, and Postnikov.
Keywords: hook length formulas for trees, k-ary trees, planes trees, labeled trees