English

Probabilistic proofs of hook length formulas involving trees

Combinatorics 2008-06-12 v2

Abstract

Recently, Han discovered two formulas involving binary trees which have the interestig property that hooklengths appear as exponents. The purpose of this note is to give a probabilistic proof of one of Han's formulas. Yang has generalized Han's results to ordered trees. We show how the probabilistic approach can also be used in Yang's setting, as well as for a generalization of Han's formula in terms of certain infinite trees.

Keywords

Cite

@article{arxiv.0805.0817,
  title  = {Probabilistic proofs of hook length formulas involving trees},
  author = {Bruce E. Sagan},
  journal= {arXiv preprint arXiv:0805.0817},
  year   = {2008}
}

Comments

Final version with proofs, 6 figures, and a section on open problems added

R2 v1 2026-06-21T10:37:57.156Z