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arXiv · 1103.4068

On Han's Hook Length Formulas for Trees

William Y. C. Chen·Oliver X. Q. Gao·Peter L. Guo
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Abstract

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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William Y. C. Chen, Oliver X. Q. Gao, Peter L. Guo. 2011-03-21. On Han's Hook Length Formulas for Trees. https://arxiv.org/abs/1103.4068

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