Hyperplane arrangements between Shi and Ish

Q2 Mathematics Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.046

Rui Duarte , António Guedes de Oliveira

引用次数: 0

Abstract

We introduce a new family of hyperplane arrangements in dimension $n \geq 3$ that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family 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 labelling. In addition, we characterise the Pak-Stanley labels of the regions of this family of hyperplane arrangements.

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Shi和Ish之间的超平面排列

我们在n≥3维中引入了一种新的超平面排列族，它既包括Shi排列，也包括Ish排列。我们证明了这个族的所有成员都有相同数量的区域-超平面的并补的连通分量-可以用Pak-Stanley标记客观地标记。此外，我们刻画了这类超平面排列的区域的Pak-Stanley标签。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

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1.30

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0.00%

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