On Han's Hook Length Formulas for Trees

Details On Han's Hook Length Formulas for Trees On Han's Hook Length Formulas for Trees

2011-03-21

arxiv.org/abs/1103.4068v1

Mathematics

Combinatorics

8 pages, 3 figures

Scientific paper

Recently, Han obtained two hook length formulas for binary trees and asked for combinatorial proofs. One of Han's formulas has been generalized to k-ary trees by Yang. Sagan has found a probabilistic proof of Yang's extension. We give combinatorial proofs of Yang's formula for k-ary trees and the other formula of Han for binary trees. Our bijections are based on the structure of k-ary trees with staircase labelings.

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