On composite lacunary polynomials and the proof of a conjecture of Schinzel

This paper completely settles a conjecture of Schinzel (formulated already by Erdos in a special case) stating that if a composite polynomial g(h(x)) has at most L terms then already h(x) must have at most t_L terms, where t_L is a function of L only. This actually sharpens the original Schinzel's conjecture. The methods are completely new and also yield an algorithm for "writing down" the possible composition factors of a general polynomial with a given number of terms.