TY - JOUR
T1 - Chambers of 2-affine arrangements and freeness of 3-arrangements
AU - Abe, Takuro
N1 - Funding Information:
Acknowledgements The author thanks Yasuhide Numata for reading the first draft of this article and pointing out a mistake. The author is grateful to the referees for the careful reading and a lot of useful comments on this article. This work is supported by JSPS Grants-in-Aid for Young Scientists (B) No. 21740014.
PY - 2013/8
Y1 - 2013/8
N2 - 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.
AB - 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.
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U2 - 10.1007/s10801-012-0393-x
DO - 10.1007/s10801-012-0393-x
M3 - Article
AN - SCOPUS:84879687362
SN - 0925-9899
VL - 38
SP - 65
EP - 78
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 1
ER -