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 formula_1, where formula_2 is a periodic function with integral period. If formula_3 is not identically zero, then the degree of formula_4 is formula_5. Equivalently, a function formula_6 is a quasi-polynomial if there exist polynomials formula_7 such that formula_8 when formula_9. The polynomials formula_10 are called the constituents of formula_11.
Examples.
which is a quasi-polynomial with degree formula_27