The stability of the family of B2-type arrangements

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We introduce the family of B2-type arrangements as a generalization of the classical Coxeter arrangement of type B2 and consider the stability and the freeness of it. We show the freeness and (semi)stability are determined by the combinatorics. Moreover, we give a partial answer to the 4-shift problem, which is a conjecture on the combinatorics and geometry induced from the B2-type arrangements.

Original languageEnglish
Pages (from-to)1193-1215
Number of pages23
JournalCommunications in Algebra
Volume37
Issue number4
DOIs
Publication statusPublished - Apr 1 2009
Externally publishedYes

Fingerprint

Arrangement
Combinatorics
Semistability
Partial
Family
Generalization

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

The stability of the family of B2-type arrangements. / Abe, Takuro.

In: Communications in Algebra, Vol. 37, No. 4, 01.04.2009, p. 1193-1215.

Research output: Contribution to journalArticle

@article{0f97e1fe64f3460d8e8b61a556d25066,
title = "The stability of the family of B2-type arrangements",
abstract = "We introduce the family of B2-type arrangements as a generalization of the classical Coxeter arrangement of type B2 and consider the stability and the freeness of it. We show the freeness and (semi)stability are determined by the combinatorics. Moreover, we give a partial answer to the 4-shift problem, which is a conjecture on the combinatorics and geometry induced from the B2-type arrangements.",
author = "Takuro Abe",
year = "2009",
month = "4",
day = "1",
doi = "10.1080/00927870802465969",
language = "English",
volume = "37",
pages = "1193--1215",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "4",

}

TY - JOUR

T1 - The stability of the family of B2-type arrangements

AU - Abe, Takuro

PY - 2009/4/1

Y1 - 2009/4/1

N2 - We introduce the family of B2-type arrangements as a generalization of the classical Coxeter arrangement of type B2 and consider the stability and the freeness of it. We show the freeness and (semi)stability are determined by the combinatorics. Moreover, we give a partial answer to the 4-shift problem, which is a conjecture on the combinatorics and geometry induced from the B2-type arrangements.

AB - We introduce the family of B2-type arrangements as a generalization of the classical Coxeter arrangement of type B2 and consider the stability and the freeness of it. We show the freeness and (semi)stability are determined by the combinatorics. Moreover, we give a partial answer to the 4-shift problem, which is a conjecture on the combinatorics and geometry induced from the B2-type arrangements.

UR - http://www.scopus.com/inward/record.url?scp=69249199555&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69249199555&partnerID=8YFLogxK

U2 - 10.1080/00927870802465969

DO - 10.1080/00927870802465969

M3 - Article

AN - SCOPUS:69249199555

VL - 37

SP - 1193

EP - 1215

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 4

ER -