The weighted hook length formula
Combinatorics
2010-06-02 v1
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.
Cite
@article{arxiv.1006.0043,
title = {The weighted hook length formula},
author = {Ionut Ciocan-Fontanine and Matjaz Konvalinka and Igor Pak},
journal= {arXiv preprint arXiv:1006.0043},
year = {2010}
}
Comments
14 pages, 4 figures