A bijective proof of the hook-length formula for standard immaculate tableaux

Author:

Gao Alice,Yang Arthur

Abstract

In this paper, we present a direct bijective proof of the hook-length formula for standard immaculate tableaux, which arose in the study of non-commutative symmetric functions. Our proof is along the spirit of Novelli, Pak and Stoyanovskiĭ’s combinatorial proof of the hook-length formula for standard Young tableaux.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference7 articles.

1. A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions;Berg, Chris;Canad. J. Math.,2014

2. The hook graphs of the symmetric groups;Frame, J. S.;Canad. J. Math.,1954

3. A bijective proof of the hook-length formula;Franzblau, D. S.;J. Algorithms,1982

4. A probabilistic proof of a formula for the number of Young tableaux of a given shape;Greene, Curtis;Adv. in Math.,1979

5. Reverse plane partitions and tableau hook numbers;Hillman, A. P.;J. Combinatorial Theory Ser. A,1976

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