Abstract
We define an n-arrangement as a finite family of hyperplanes through the origin in C +1. In [11] and [12] we studied the free arrangement and defined its structure sequence (their definitions will be given again in Sect. 2). In this article we say the generalized exponents instead of the structure sequence. Let (d o , d 1 . . . . . d,) be the generalized exponents of a free n-arrangement X. Let ]XJ = U H. Our main result is HEX
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