The weighted hook length formula

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Ciocan-Fontanine, Ionut¹  Konvalinka, Matjaz²  Pak, Igor³ 

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

[3] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

关键词: Hook-length formula;    Weighted analogue;    Bijective proof;   

DOI  :  10.1016/j.jcta.2011.02.004

来源: Elsevier

【 摘 要 】

Based on the ideas in Ciocan-Fontanine, Konvalinka and Pak (2009) [5], 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 Greene. Nijenhuis and Wilf (1979) [15], as well as the q-walk of Kerov (1993) [20]. Further applications are also presented. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free