Multivariate approximation and one problem of combinatorial number theory

Subdivision schemes known since classical works of De Rham and developed in 90-s by Dyn, Micchelli, Dahmen, Cohen, Oswald, etc. provide a very popular method of multivariate approximation and an efficient toolbox for generating curves and surfaces. We show how the subdivision schemes can be applied to one problem of number theory (computing of the binary partition function) and to classifying special cyclotomic polynomials.