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$q$-Hook formula of Gansner type for a generalized Young diagram

Abstract : 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.
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Kento Nakada. $q$-Hook formula of Gansner type for a generalized Young diagram. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.685-696. ⟨hal-01185376⟩

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