On the computation of hilbert—Poincaré series

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Abstract

We prove a theorem, which provides a formula for the computation of the Poincaré series of a monomial ideal ink[X1,⋯, Xn], via the computation of the Poincaré series of some monomial ideals ink[X 1,⋯, Xi,⋯, Xn]. The complexity of our algorithm is optimal for Borel-normed ideals and an implementation in CoCoA strongly confirms its efficiency. An easy extension computes the Poincaré series of graded modules over standard algebras.