  We compare each coefficient of the reduced characteristic polynomial of a
simple arrangement and that of its Ziegler restriction. As a consequence we can
show that the former is not less than the latter in the category of tame
arrangements. This is a generalization of Yoshinaga's freeness criterion for
3-arrangements and also the recent result by the author and Yoshinaga. As a
corollary, we can prove that a free arrangement is a minimal chamber
arrangement, and we can give a freeness criterion in terms of chambers in the
category of tame arrangements.
