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

is a periodic function with integral period.

is not identically zero, then the degree of

Equivalently, a function

is a quasi-polynomial if there exist polynomials

mod

The polynomials

are called the constituents of

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