## Abstract

The famous hook-length formula is a simple consequence of the branching rule for the hook lengths. While the Greene-Nijenhuis-Wilf probabilistic proof is the most famous proof of the rule, it is not completely combinatorial, and a simple bijection was an open problem for a long time. In this extended abstract, we show an elegant bijective argument that proves a stronger, weighted analogue of the branching rule. Variants of the bijection prove seven other interesting formulas. Another important approach to the formulas is via weighted hook walks; we discuss some results in this area. We present another motivation for our work: J-functions of the Hilbert scheme of points.

Original language | English (US) |
---|---|

Pages | 259-270 |

Number of pages | 12 |

State | Published - Dec 1 2010 |

Event | 22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 - San Francisco, CA, United States Duration: Aug 2 2010 → Aug 6 2010 |

### Other

Other | 22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 |
---|---|

Country | United States |

City | San Francisco, CA |

Period | 8/2/10 → 8/6/10 |

## Keywords

- Bijective proofs
- Hilbert scheme of points
- Hook-length formula