Hilbert series
= Hilbert series
{wiki=Hilbert_series_and_Hilbert_polynomial}
For a graded module $M=\bigoplus_{n\ge0}M_n$ whose pieces have finite length, its Hilbert series is
$$
H_M(z)=\sum_{n\ge0}\operatorname{length}(M_n)z^n.
$$
= Hilbert series
{wiki=Hilbert_series_and_Hilbert_polynomial}
For a graded module $M=\bigoplus_{n\ge0}M_n$ whose pieces have finite length, its Hilbert series is
$$
H_M(z)=\sum_{n\ge0}\operatorname{length}(M_n)z^n.
$$