### Abstract

The purpose of this paper is to present an algorithm which generates linear extensions for a generalized Young diagram, in the sense of D. Peterson and R. A. Proctor, with uniform probability. This gives a proof of a D. Peterson's hook formula for the number of reduced decompositions of a given minuscule elements.

Original language | English |
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Pages | 933-940 |

Number of pages | 8 |

Publication status | Published - 2010 |

Externally published | Yes |

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 |
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Country | United States |

City | San Francisco, CA |

Period | 8/2/10 → 8/6/10 |

### Keywords

- Algorithm
- Generalized Young diagrams
- Kac-Moody Lie algebra
- Linear extension

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Nakada, K., & Okamura, S. (2010).

*An algorithm which generates linear extensions for a generalized Young diagram with uniform probability*. 933-940. Paper presented at 22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10, San Francisco, CA, United States.