Quasi-polynomial

In mathematics, a quasi-polynomial (pseudo-polynomial) is a generalization of polynomials. While the coefficients of a polynomial come from a ring, the coefficients of quasi-polynomials are instead periodic functions with integral period. Quasi-polynomials appear throughout much of combinatorics as the enumerators for various objects.

A quasi-polynomial can be written as, where is a periodic function with integral period. If is not identically zero, then the degree of q is d. Equivalently, a function is a quasi-polynomial if there exist polynomials such that when . The polynomials are called the constituents of f.