Geodesic
Chambers of 2-affine arrangements and freeness of 3-arrangements
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 65-78.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: hyperplane arrangements, free arrangements, chambers of arrangements, characteristic polynomial, exponents of multiarrangements 
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Abe, Takuro. Chambers of 2-affine arrangements and freeness of 3-arrangements. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 65-78. http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a7/