A Simple Bijection For The Regions Of The Shi Arrangement Of Hyperplanes
, 1997 . The Shi arrangement Sn is the arrangement of affine hyperplanes in R n of the form x i \Gamma x j = 0 or 1, for 1 i ! j n. It dissects R n into (n+1) n\Gamma1 regions, as was first proved by Shi. We give a simple bijective proof of this result.
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Equivariant multiplicities of Coxeter arrangements and invariant basesLet A be an irreducible Coxeter arrangement and W be its Coxeter group. Then W naturally acts on A. A multiplicity m : A → Z is said to be equivariant when m is constant on each W-orbit of A. In this article, we prove that the multi-derivation module D(A, m) is a free module whenever m is equivariant by explicitly constructing a basis, which ...
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