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Chambers of 2-affine arrangements and freeness of 3-arrangements. (English) Zbl 1284.52022

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.

MSC:

52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
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