Dn型通有构形的特征多项式

doi:10.6040/j.issn.1671-9352.0.2021.611

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 106-110.doi: 10.6040/j.issn.1671-9352.0.2021.611

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D_n型通有构形的特征多项式

张苗,强晶晶,高瑞梅^*

长春理工大学数学与统计学院, 吉林长春 130022

发布日期:2022-10-06
作者简介:张苗(1998— ),女,硕士研究生,研究方向为超平面构形. E-mail:damiao82@163.com*通信作者简介: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
基金资助:
国家自然科学基金资助项目(11501051);吉林省教育厅科学技术研究项目(JJKH20220719KJ)

Characteristic polynomials for the generic arrangements of type D_n

ZHANG Miao, QIANG Jing-jing, GAO Rui-mei^*

School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, Jilin, China

Published:2022-10-06

摘要/Abstract

摘要： 设W是n维欧氏空间中的D_n型Weyl群,以W的正根为法向量的超平面形成的通有构形称为D_n型通有构形,记为A(D_n)。首先建立了不含自环的符号图与A(D_n)的子构形的一一对应关系;其次,研究了一个符号圈线性相关的充要条件;最后从符号图的角度给出A(D_n)的子构形线性无关的充要条件。在此基础上,给出A(D_n)及其子构形的特征多项式的具体计算方法。

关键词: D_n型通有构形, 符号图, 特征多项式

Abstract: Assume that W is a Weyl group of type D_n in a Euclidean space with dimension n. A generic arrangement of type D_n is one that consists of hyperplanes whose normal vectors are the positive roots of W. It is denoted by A(D_n). To begin with, a one-to-one connection between the signed graphs with no loops and the sub-arrangements of A(D_n) is established. Then, the sufficient and necessary condition for the linear dependence of signed circles are studied. In the end, from the point of view of signed graphs, the necessary and sufficient conditions for linear independence of sub-arrangements of A(D_n) are given. On this basis, the concrete calculation method of characteristic polynomials of A(D_n) and its sub-arrangements are given.

Key words: generic arrangement of type D_n, signed graph, characteristic polynomial

中图分类号:

O189.1

张苗,强晶晶,高瑞梅. D_n型通有构形的特征多项式[J]. 《山东大学学报(理学版)》, 2022, 57(10): 106-110.

ZHANG Miao, QIANG Jing-jing, GAO Rui-mei. Characteristic polynomials for the generic arrangements of type D_n[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 106-110.

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D_n型通有构形的特征多项式

Characteristic polynomials for the generic arrangements of type D_n

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Dn型通有构形的特征多项式

Characteristic polynomials for the generic arrangements of type Dn

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D_n型通有构形的特征多项式

Characteristic polynomials for the generic arrangements of type D_n