Probabilistic proofs of hook length formulas involving trees

Details Probabilistic proofs of hook length formulas involving trees Probabilistic proofs of hook length formulas involving trees

2008-05-07

arxiv.org/abs/0805.0817v2

Mathematics

Combinatorics

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

Scientific paper

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.

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