Rational dependence among Hilbert and Poincaré series
In this paper one shows that certain important sets of formal power series are mutually related by rational formulae. Adding also results of the same nature of J.-E. Roos, J.-M. Lemaire, C. Löfwall, G. Levin there are seventeen such sets, among which: Poincaré series of loop spaces on finite CW complexes, Poincaré series of noetherian local rings, Hilbert series of finitely presented graded algebras, and also remarkable subsets of these. In particular, these results show that the classification of those series which occur in one set gives the answer to the classification problem for all the others.
rational relation of Hilbert series and Poincaré series
scientific article; zbMATH DE number 3918517
scientific article