The Shi arrangement and the Ish arrangement by Drew Armstrong, Brendon Rhoades

“…This paper is about two arrangements of hyperplanes. The first — the Shi arrangement — was introduced by Jian-Yi Shi to describe the Kazhdan-Lusztig cells in the affine Weyl group of type A. …”
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Gallery Posets of Supersolvable Arrangements by Thomas McConville

“…We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of reduced words. …”
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