Shi和Ish之间的超平面排列

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

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引用次数: 0

摘要

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。

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Hyperplane arrangements between Shi and Ish

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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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.