### Abstract

In [58], Shi proved Lusztigâ€™s conjecture that the number of two-sided cells for the affine Weyl group of type A_{n-1} is the number of partitions of n. As a byproduct, he introduced the Shi arrangement of hyperplanes and found a few of its remarkable properties. The Shi arrangement has since become a central object in algebraic combinatorics. This article is intended to be a fairly gentle introduction to the Shi arrangement, intended for readers with a modest background in combinatorics, algebra, and Euclidean geometry.

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

Title of host publication | Association for Women in Mathematics Series |

Publisher | Springer |

Pages | 75-113 |

Number of pages | 39 |

DOIs | |

State | Published - Jan 1 2019 |

### Publication series

Name | Association for Women in Mathematics Series |
---|---|

Volume | 16 |

ISSN (Print) | 2364-5733 |

ISSN (Electronic) | 2364-5741 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Gender Studies

### Cite this

*Association for Women in Mathematics Series*(pp. 75-113). (Association for Women in Mathematics Series; Vol. 16). Springer. https://doi.org/10.1007/978-3-030-05141-9_3

**A Survey of the Shi Arrangement.** / Fishel, Susanna.

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

*Association for Women in Mathematics Series.*Association for Women in Mathematics Series, vol. 16, Springer, pp. 75-113. https://doi.org/10.1007/978-3-030-05141-9_3

}

TY - CHAP

T1 - A Survey of the Shi Arrangement

AU - Fishel, Susanna

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In [58], Shi proved Lusztigâ€™s conjecture that the number of two-sided cells for the affine Weyl group of type An-1 is the number of partitions of n. As a byproduct, he introduced the Shi arrangement of hyperplanes and found a few of its remarkable properties. The Shi arrangement has since become a central object in algebraic combinatorics. This article is intended to be a fairly gentle introduction to the Shi arrangement, intended for readers with a modest background in combinatorics, algebra, and Euclidean geometry.

AB - In [58], Shi proved Lusztigâ€™s conjecture that the number of two-sided cells for the affine Weyl group of type An-1 is the number of partitions of n. As a byproduct, he introduced the Shi arrangement of hyperplanes and found a few of its remarkable properties. The Shi arrangement has since become a central object in algebraic combinatorics. This article is intended to be a fairly gentle introduction to the Shi arrangement, intended for readers with a modest background in combinatorics, algebra, and Euclidean geometry.

UR - http://www.scopus.com/inward/record.url?scp=85071492168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071492168&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-05141-9_3

DO - 10.1007/978-3-030-05141-9_3

M3 - Chapter

AN - SCOPUS:85071492168

T3 - Association for Women in Mathematics Series

SP - 75

EP - 113

BT - Association for Women in Mathematics Series

PB - Springer

ER -