Hilbert function

The Hilbert function of a graded module $M={⨁}_n{M}_n$ over a field is $n\mapsto {\dim }_k{M}_n$. Its generating function is the Hilbert series.

A quasipolynomial is a function $f:\mathbb{Z}\to \mathbb{C}$ for which there are polynomials $P_0,\dots ,P_{m-1}$ such that $f(n)=P_r(n)$ whenever $n\equiv r(\mathrm{mod}m)$. The least possible positive $m$ is its period.