Hook Length Formulas for Trees by Han's Expansion

Details Hook Length Formulas for Trees by Han's Expansion Hook Length Formulas for Trees by Han's Expansion

2009-03-19

arxiv.org/abs/0903.3342v1

Mathematics

Combinatorics

16 pages

Scientific paper

Recently Han obtained a general formula for the weight function corresponding to the expansion of a generating function in terms of hook lengths of binary trees. In this paper, we present 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.

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