简单相连多边形对应的图构形的特征多项式

doi:10.6040/j.issn.1671-9352.0.2015.569

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (10): 72-77.doi: 10.6040/j.issn.1671-9352.0.2015.569

简单相连多边形对应的图构形的特征多项式

高瑞梅,李喆^*

长春理工大学理学院, 吉林长春 130022

收稿日期:2015-11-27 出版日期:2016-10-20 发布日期:2016-10-17
通讯作者: 李喆(1981— ), 女, 博士, 副教授,研究方向为计算机代数. E-mail:zheli200809@163.com E-mail:gaorm135@nenu.edu.cn
作者简介:高瑞梅(1983— ),女,博士,讲师,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“十二五”科学技术研究项目(吉教科合字［2015］第52号);长春理工大学科技创新基金项目(XJJLG-2014-01)

The characteristic polynomials of the graphical arrangements corresponding to the simply-connected polygons

College of Science, Changchun University of Science and Technology, Changchun 130022, Jilin, China

Received:2015-11-27 Online:2016-10-20 Published:2016-10-17

摘要/Abstract

摘要： 图构形是构形领域研究的与图相关的一类超平面构形。给出了多边形简单相连和点相连的定义, 研究简单相连多边形对应的图构形的特征多项式, 并给出其具体表达式。通过具体例子说明多边形连接方式和连接顺序的不同对图构形中超平面相交关系的影响。

关键词: 特征多项式, π-等价, 图构形, 超平面构形, L-等价

Abstract: The graphical arrangements are the arrangements relative to graphs. The definitions of simply-connected and point-connected of the polygons were given, the characteristic polynomials of the graphical arrangements corresponding to the simply-connected polygons were studied, and the specific forms of the characteristic polynomials were obtained. By using the concrete example, the effect on the intersection relationships of the hyperplanes in an arrangement by the different connection methods or the different sequential manners of the polygons was pointed out.

Key words: hyperplane arrangement, characteristic polynomial, L-equivalent, π-equivalent, graphical arrangement

中图分类号:

O189

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.

参考文献

[1] ORLIK P, TERAO H. Arrangements of hyperplanes[M] // Grundlehren der Mathematischen Wissenschaften. Berlin: Springer-Verlag, 1992:1-325.
[2] YOSHINAGA M. Characterization of a free arrangement and conjecture of Edelman and Reiner[J]. Inventiones Mathematicae, 2004, 157(2):449-454.
[3] ABE T, TERAO H. The freeness of Shi-Catalan arrangements[J]. European Journal of Combinatorics, 2011, 32(8):1191-1198.
[4] GAO Ruimei, PEI Donghe, TERAO H. The Shi arrangement of the type D_l[J]. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2012, 88:41-45.
[5] SUYAMA D, TERAO H. The Shi arrangements and the Bernoulli polynomials[J]. The Bulletin of the London Mathematical Society, 2012, 44(2):563-570.
[6] BARAKAT M, CUNTZ M. Coxeter and crystallographic arrangements are inductively free[J]. Advances in Mathematics, 2012, 229(1):691-709.
[7] ABE T, TERAO H. Simple-root bases for Shi arrangements[J]. Journal of Algebra, 2015, 422(6):89-104.
[8] 高瑞梅. G2型Shi-Catalan构形的自由性[J]. 山东大学学报(理学版), 2014, 49(12):66-70. GAO Ruimei. The freeness of Shi-Catalan arrangements of type G2[J]. Journal of Shandong University(Natural Science), 2014, 49(12):66-70.
[9] STANLEY R P. Supersolvable lattices[J]. Algebra Universalis, 1972, 2(1):197-217.
[10] EDELMAN P H, REINER V. Free hyperplane arrangements between A_n-1 and B_n[J]. Mathematische Zeitschrift, 1994, 215(1):347-365.
[11] JIANG Tan, YAU S S T, YEH L Y. Simple geometric characterization of supersolvable arrangements[J]. The Rocky Mountain Journal of Mathematics, 2001, 31(1):303-312.
[12] JIANG Guangfeng, YU Jianming. Supersolvability of complementary signed-graphic hyperplane arrangements[J]. The Australasian Journal of Combinatorics, 2004, 30:261-274.
[13] BERTHOMÉ P, CORDOVIL R, FORGE D, et al. An elementary chromatic reduction for gain graphs and special hyperplane arrangements[J]. Electronic Journal of Combinatorics, 2009, 16(1):1878+892.
[14] GAO Ruimei, PEI Donghe. The supersolvable order of hyperplanes of an arrangement[J]. Communications in Mathematical Research, 2013, 29(3):231-238.
[15] MU Lili, STANLEY R P. Supersolvability and freeness for ψ-graphical arrangements[J]. Discrete and Computational Geometry, 2015, 5:96-126.
[16] STANLEY R P. Valid orderings of real hyperplane arrangements[J]. Discrete and Computational Geometry, 2015, 53(4):965-970.
[17] MACINIC A D, PAPADIMA S. On the monodromy action on milnor fibers of graphic arrangements[J].Topology and its Applications, 2009, 156(4):761-774.
[18] ABE T, TERAO H, Wakefield M. The characteristic polynomial of a multiarrangement[J]. Advances in Mathematics, 2007, 215(2):825-838.
[19] ATHANASIADIS C A. Characteristic polynomials of subspace arrangements and finite fields[J]. Advances in Mathematics, 1996, 122(2):193-233.
[20 ] STANLEY R P. An introduction to hyperplane arrangements[M]. New Jersey: IAS/Park City Math Ser, 2004.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

简单相连多边形对应的图构形的特征多项式

The characteristic polynomials of the graphical arrangements corresponding to the simply-connected polygons

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 8

多维度评价

本文评价

推荐阅读 0

[1]	高瑞梅,初颖. Weyl构形A_n-1和B_n之间的构形的自由性[J]. 山东大学学报（理学版）, 2018, 53(6): 70-75.
[2]	高瑞梅1,裴东河2. 构形的特征多项式和超可解性的算法[J]. 山东大学学报（理学版）, 2014, 49(2): 51-57.
[3]	曹海松，伍俊良 . 矩阵特征值在椭圆形区域上的估计[J]. J4, 2012, 47(10): 49-53.
[4]	张爽,裴东河,高瑞梅. 广义p-通有中心平行构形[J]. J4, 2010, 45(8): 32-35.
[5]	崔秀鹏裴东河高瑞梅. S²球构形的分类及一类特殊球构形的特征多项式[J]. J4, 2010, 45(2): 10-13.
[6]	孙志业,裴东河,高瑞梅. 构形和拟阵的同构映射及关于超可解的几个性质[J]. J4, 2009, 44(1): 59-62 .
[7]	张胜礼,潘正华,冯善状 . 树的最大特征值的序[J]. J4, 2008, 43(6): 37-43 .
[8]	贾志刚,赵建立,张凤霞 . 广义对称矩阵的特征问题及其奇异值分解[J]. J4, 2007, 42(12): 15-18 .