English

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}
}

Comments

16 pages

R2 v1 2026-06-21T12:42:22.608Z