  A univariate polynomial f over a field is decomposable if it is the
composition f = g(h) of two polynomials g and h whose degree is at least 2. We
determine the dimension (over an algebraically closed field) of the set of
decomposables, and an approximation to their number over a finite field. The
tame case, where the field characteristic p does not divide the degree n of f,
is reasonably well understood, and we obtain exponentially decreasing error
bounds. The wild case, where p divides n, is more challenging and our error
bounds are weaker.

Commutative Algebra;Combinatorics