Hilbert function
In commutative algebra, the Hilbert function of a graded commutative algebra or graded module is a polynomial in one variable that measures the rate of growth of the dimensions of its homogeneous components.
When the graded algebra is generated by elements in the first gradation, this is the Hilbert polynomial. In other cases, it is a quasi-polynomial; that is, there is a finite collection of polynomials which give the dimension of the homogeneous and the polynomial to be used is determined by the conjugacy class of the gradation.
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