Rational dependence among Hilbert and Poincaré series
type: Item
instance of: scholarly article
title: Rational dependence among Hilbert and Poincaré series
zbMATH Open document ID: 0575.13008
DOI: 10.1016/0022-4049(85)90005-2
author: David J. Anick
author: Tor H. Gulliksen
published in: Journal of Pure and Applied Algebra
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 13D99
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 55P45
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 16W50
zbMATH DE Number: 3918517
zbMATH Keywords: rational relation of Hilbert series and Poincaré series
zbMATH Keywords: loop spaces on finite CW complexes
zbMATH Keywords: noetherian local rings
zbMATH Keywords: finitely presented graded algebras
reviewed by: Nicolae Pop
MaRDI profile type: Publication
full work available at URL: 0022-4049(85)90005-2
OpenAlex ID: W1978309514
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description: scientific article; zbMATH DE number 3918517