On the computation of hilbert—Poincaré series

  • Anna Maria Bigatti
  • Massimo Caboara
  • Lorenzo Robbiano


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[X1,⋯, 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.


Hilbert functions Poincaré series Borel-normed ideals 


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Anna Maria Bigatti
    • 1
  • Massimo Caboara
    • 1
  • Lorenzo Robbiano
    • 1
  1. 1.Departimento di Matematica dell'Universitá di GenovaGenovaItaly

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