Between Shi and Ish

  title={Between Shi and Ish},
  author={Rui Duarte and Ant{\'o}nio Guedes de Oliveira},
  journal={Discrete Mathematics},
Abstract We introduce a new family of hyperplane arrangements in dimension n ≥ 3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of a given subfamily have the same number of regions – the connected components of the complement of the union of the hyperplanes – which can be bijectively labeled with the Pak–Stanley labeling. In addition, we show that, in the cases of the Shi and the Ish arrangements, the number of labels with reverse centers of a… CONTINUE READING
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