Preprint
<p>We introduce a new family of hyperplane arrangements in dimension $n\geq3$ 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 <em>bijectively</em>\ 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 <em>reverse centers</em>\ of a given length is equal, and conjecture that the same happens with all of the members of the family.\ </p> <p>\ </p>
Ant\ de Oliveira
Rui Duarte
Publication
Year of publication: 2017
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ArXiv1703.02509.pdf245.26 KB