Hilbert series and Hilbert polynomial
POLYNOMIAL FUNCTION WITH RATIONAL COEFFICIENTS WHOSE VALUES AGREE, FOR SUFFICIENTLY LARGE ARGUMENT, WITH THE DIMENSIONS OF GRADED COMPONENTS OF A GRADED ALGEBRA
Hilbert function; Hilbert series; Hilbert regularity; Hilbert polynomial; Hilbert characteristic function
In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a field are three strongly related notions which measure the growth of the dimension of the homogeneous components of the algebra.