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


Authors: Alice L. L. Gao and Arthur L. B. Yang
Journal: Proc. Amer. Math. Soc. 144 (2016), 989-998
MSC (2010): Primary 05E05
DOI: https://doi.org/10.1090/proc/12899
Published electronically: September 24, 2015
MathSciNet review: 3447653
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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.


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Additional Information

Alice L. L. Gao
Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
Email: gaolulublue@mail.nankai.edu.cn

Arthur L. B. Yang
Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
Email: yang@nankai.edu.cn

DOI: https://doi.org/10.1090/proc/12899
Keywords: Composition, hook, hook{-}length formula, immaculate tableau, standard immaculate tableau
Received by editor(s): March 14, 2015
Published electronically: September 24, 2015
Communicated by: Patricia Hersh
Article copyright: © Copyright 2015 American Mathematical Society