Hook Length Formulas for Trees by Han's Expansion
Combinatorics
2009-03-20 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0903.3342,
title = {Hook Length Formulas for Trees by Han's Expansion},
author = {William Y. C. Chen and Oliver X. Q. Gao and Peter L. Guo},
journal= {arXiv preprint arXiv:0903.3342},
year = {2009}
}
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16 pages