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arXiv · 1006.0043

The weighted hook length formula

Ionut Ciocan-Fontanine·Matjaz Konvalinka·Igor Pak
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Abstract

Based on the ideas in [CKP], we introduce the weighted analogue of the branching rule for the classical hook length formula, and give two proofs of this result. The first proof is completely bijective, and in a special case gives a new short combinatorial proof of the hook length formula. Our second proof is probabilistic, generalizing the (usual) hook walk proof of Green-Nijenhuis-Wilf, as well as the q-walk of Kerov. Further applications are also presented.

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BibTeXRIS

Ionut Ciocan-Fontanine, Matjaz Konvalinka, Igor Pak. 2010-06-01. The weighted hook length formula. https://arxiv.org/abs/1006.0043

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