Counting decomposable polynomials with integer coefficients

A polynomial over a ring is called decomposable if it is a composition of two nonlinear polynomials. In this paper, we give sharp lower and upper bounds for the number of decomposable polynomials with integer coefficients of fixed degree and bounded height. Moreover, we determine the main contributions to decomposable polynomials. These results imply that almost all integer polynomials are indecomposable.