A Survey of the Shi Arrangement

Research output: Chapter in Book/Report/Conference proceedingChapter


In [58], Shi proved Lusztig’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.

Original languageEnglish (US)
Title of host publicationAssociation for Women in Mathematics Series
Number of pages39
StatePublished - Jan 1 2019

Publication series

NameAssociation for Women in Mathematics Series
ISSN (Print)2364-5733
ISSN (Electronic)2364-5741

ASJC Scopus subject areas

  • Mathematics(all)
  • Gender Studies

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    Fishel, S. (2019). A Survey of the Shi Arrangement. In 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