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

dmtcs:2684 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2684
$q$-Hook formula of Gansner type for a generalized Young diagramArticle

Authors: Kento Nakada 1

  • 1 Wakkanai Hokusei Gakuen University

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.

https://doi.org/10.46298/dmtcs.2684
Source: HAL:hal-01185376v1
Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Generalized Young diagrams,Trace generating functions,$q$-hook formula,Kac-Moody Lie algebra,P. MacMahon's identity,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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