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山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (6): 70-75.doi: 10.6040/j.issn.1671-9352.0.2017.644

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Weyl构形An-1和Bn之间的构形的自由性

高瑞梅,初颖*   

  1. 长春理工大学理学院, 吉林 长春 130022
  • 收稿日期:2017-12-19 出版日期:2018-06-20 发布日期:2018-06-13
  • 作者简介:高瑞梅(1983— ), 女, 博士, 副教授, 研究方向为奇点理论和超平面构形. E-mail:gaorm135@nenu.edu.cn*通信作者简介:初颖(1984— ), 女, 博士, 讲师, 研究方向为奇异椭圆方程的求解问题. E-mail:chuying_12345@sina.com
  • 基金资助:
    国家自然科学基金资助项目(11501051);吉林省科技发展计划项目优秀青年人才基金项目(20180520025JH)

Freeness of arrangements between the Weyl arrangements of types An-1 and Bn

GAO Rui-mei, CHU Ying*   

  1. Department of Science, Changchun University of Science and Technology, Changchun 130022, Jilin, China
  • Received:2017-12-19 Online:2018-06-20 Published:2018-06-13

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摘要： Weyl群的反射超平面形成的集合称为该群对应的Weyl构形。设符号An-1和Bn分别表示An-1型和Bn型Weyl构形。若构形A满足An-1⊂A⊂Bn, 则称A为An-1和Bn之间的构形。本文首先研究了阈图,给出构造阈图的一种方法。 然后,利用阈图研究了An-1和Bn之间的构形的自由性。给出结论:对于满足|An-1|n|的任意整数k, 均存在An-1和Bn之间的自由构形, 其基数为k。同时也给出An-1和Bn之间的非自由构形的类似的结论。

关键词: 图构形, 自由性, Weyl构形, 阈图, 符号图

Abstract: The set of reflecting hyperplanes of a Weyl group is called Weyl arrangement. Assume the notations An-1 and Bn denote the Weyl arrangements of types An-1 and Bn respectively. The arrangement A which satisfies An-1⊂A⊂Bn is called the arrangement between An-1 and Bn. Firstly, we study threshold graphs, and give a construction for threshold graphs. Secondly, we study the freeness of the arrangements between An-1 and Bn by using threshold graphs. And we conclude: for any integer k satisfying |An-1|n|, there exists a free arrangement between An-1 and Bn with cardinality k. A similar conclusion for the non-freeness arrangements between An-1 and Bn is given.

Key words: Weyl arrangement, threshold graph, signed graph, graphical arrangement, freeness

中图分类号: 

  • O189
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[1] 高瑞梅,李喆. 简单相连多边形对应的图构形的特征多项式[J]. 山东大学学报（理学版）, 2016, 51(10): 72-77.
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