### 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 |
---|---|

Title of host publication | FPSAC'10 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics |

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 |
---|---|

Country | United States |

City | San Francisco, CA |

Period | 8/2/10 → 8/6/10 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*FPSAC'10 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics*(pp. 933-940)

**An algorithm which generates linear extensions for a generalized Young diagram with uniform probability.** / Nakada, Kento; Okamura, Shuji.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*FPSAC'10 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics.*pp. 933-940, 22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10, San Francisco, CA, United States, 8/2/10.

}

TY - GEN

T1 - An algorithm which generates linear extensions for a generalized Young diagram with uniform probability

AU - Nakada, Kento

AU - Okamura, Shuji

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Algorithm

KW - Generalized Young diagrams

KW - Kac-Moody Lie algebra

KW - Linear extension

UR - http://www.scopus.com/inward/record.url?scp=84860505027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860505027&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84860505027

SP - 933

EP - 940

BT - FPSAC'10 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics

ER -