Signed-eliminable graphs and free multiplicities on the braid arrangement

被引：11

作者：

Abe, Takuro ^{[1
]}

Nuida, Koji ^{[2
]}

Numata, Yasuhide ^{[3
]}

机构：

[1] Kyoto Univ, Dept Math, Sakyo Ku, Kyoto 606852, Japan

[2] Natl Inst Adv Ind Sci & Technol, Res Ctr Informat Secur, Chiyoda Ku, Tokyo 1010021, Japan

[3] Wakkanai Hokusei Gakuen Univ, Fac Integrated Media, Wakkanai, Hokkaido 0970013, Japan

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2009年 / 80卷

关键词：

HYPERPLANE ARRANGEMENTS; COXETER ARRANGEMENTS; DEFORMATIONS;

D O I：

10.1112/jlms/jdp019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define specific multiplicities on the braid arrangement by using signed graphs. To consider their freeness, we introduce the notion of signed-eliminable graphs as a generalization of Stanley's classification theory of free graphic arrangements by chordal graphs. This generalization gives us a complete classification of the free multiplicities defined above. As an application, we prove one direction of a conjecture of Athanasiadis on the characterization of the freeness of certain deformations of the braid arrangement in terms of directed graphs.

引用

页码：121 / 134

页数：14

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