Abstract
Which Hilbert polynomials for an m-primary ideal I in a d-dimensional, (d > 0), local Cohen-Macaulay ring (R, m) determine Heilbert function of I? For example, if we denote the Hilbert function giving the length of R/I n by H I (n) and the corresponding polynomial by p I (X), then any m -primary ideal I having Hilbert polynomial \(p_I(X) = \lambda \left( {X + \mathop d\limits_d - 1} \right)\), has Hilbert function \(H_I = \lambda \left( {n + \mathop d\limits_d - 1} \right)\) for all n > 0 and, in addition, I must be generated by d elements.
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