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$q$-Hook formula of Gansner type for a generalized Young diagram
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009) Cet article a éte moissonné depuis la source Episciences

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The purpose of this paper is to present the $q$-hook formula of Gansner type for a generalized Young diagram in the sense of D. Peterson and R. A. Proctor. This gives a far-reaching generalization of a hook length formula due to J. S. Frame, G. de B. Robinson, and R. M. Thrall. Furthurmore, we give a generalization of P. MacMahon's identity as an application of the $q$-hook formula. 
@article{DMTCS_2009_special_256_a6,
     author = {Nakada, Kento},
     title = {$q${-Hook} formula of {Gansner} type for a generalized {Young} diagram},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2009},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     doi = {10.46298/dmtcs.2684},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2684/}
}
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Nakada, Kento. $q$-Hook formula of Gansner type for a generalized Young diagram. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi: 10.46298/dmtcs.2684

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