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Between She and Ish

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 &mdash;- the connected components of the complement of the union of the hyperplanes &mdash;- which can be <em>bijectively</em>\&nbsp;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>\&nbsp;of a given length is equal, and conjecture that the same happens with all of the members of the family.\&nbsp;</p> <p>\&nbsp;</p>

Ant\ de Oliveira

Rui Duarte

Publication

Year of publication: 2017

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