  A Weyl arrangement is the arrangement defined by the root system of a finite
Weyl group. When a set of positive roots is an ideal in the root poset, we call
the corresponding arrangement an ideal subarrangement. Our main theorem asserts
that any ideal subarrangement is a free arrangement and that its exponents are
given by the dual partition of the height distribution, which was conjectured
by Sommers-Tymoczko. In particular, when an ideal subarrangement is equal to
the entire Weyl arrangement, our main theorem yields the celebrated formula by
Shapiro, Steinberg, Kostant, and Macdonald. Our proof of the main theorem
heavily depends on the theory of free arrangements and thus greatly differs
from the earlier proofs of the formula.
