The Shi arrangements and the Bernoulli polynomials

Details The Shi arrangements and the Bernoulli polynomials The Shi arrangements and the Bernoulli polynomials

2011-03-16

arxiv.org/abs/1103.3214v3

Mathematics

Combinatorics

We fixed a typo

Scientific paper

The braid arrangement is the Coxeter arrangement of the type $A_\ell$. The Shi arrangement is an affine arrangement of hyperplanes consisting of the hyperplanes of the braid arrangement and their parallel translations. In this paper, we give an explicit basis construction for the derivation module of the cone over the Shi arrangement. The essential ingredient of our recipe is the Bernoulli polynomials.

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