Chambers of 2-affine arrangements and freeness of 3-arrangements

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We give a lower bound on the number of chambers divided by a family of lines in the real plane. Also, a sufficient condition for 3-arrangements to be free is given in terms of chambers. To prove them, we give the upper bound on differences of exponents for balanced 2-multiarrangements in terms of the cardinality of hyperplanes.

Original languageEnglish
Pages (from-to)65-78
Number of pages14
JournalJournal of Algebraic Combinatorics
Volume38
Issue number1
DOIs
Publication statusPublished - Aug 1 2013

Fingerprint

Hyperplane
Cardinality
Arrangement
Exponent
Lower bound
Upper bound
Line
Sufficient Conditions
Family

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

Cite this

Chambers of 2-affine arrangements and freeness of 3-arrangements. / Abe, Takuro.

In: Journal of Algebraic Combinatorics, Vol. 38, No. 1, 01.08.2013, p. 65-78.

Research output: Contribution to journalArticle

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