### 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.

Original language | English |
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Pages | 685-696 |

Number of pages | 12 |

Publication status | Published - Dec 1 2009 |

Externally published | Yes |

Event | 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, Austria Duration: Jul 20 2009 → Jul 24 2009 |

### Other

Other | 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 |
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Country | Austria |

City | Linz |

Period | 7/20/09 → 7/24/09 |

### Keywords

- Generalized Young diagrams
- Kac-Moody Lie algebra
- P. MacMahon's identity
- Q-hook formula
- Trace generating functions

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Nakada, K. (2009).

*Q-hook formula of Gansner type for a generalized Young diagram*. 685-696. Paper presented at 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09, Linz, Austria.