The weighted hook length formula

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 [GNW1], as well as the q-walk of Kerov and the (q, t)-walk of Garsia-Haiman [Ker1, GH]. Further applications are also presented.

• Type: Journal
• Year: 2011
• Where: JCT
• Authors: Ionut Ciocan-Fontanine, Matjaz Konvalinka, Igor Pak
• Keywords: Classical Hook Length, Hook Length Formula, JCT 2011, Short Combinatorial Proof