Extremal properties of Hilbert functions
type: Item
instance of: scholarly article
title: Extremal properties of Hilbert functions
zbMATH Open document ID: 0908.13009
author: Vesselin Gasharov
published in: Illinois Journal of Mathematics
publication date: 1999-03-22T00:00:00Z
review text: Macaulay characterized Hilbert functions of graded quotients of polynomial rings. Kruskal and Katona have characterized \(f\)-vectors of simplicial complexes or, equivalently, Hilbert functions of graded quotients of the exterior algebra. Gotzmann's persistence theorem states that a space of \(d\)-forms, which is extremal in Macaulay's theorem, generates an extremal space of \((d+1)\)-forms. Aramova, Herzog and Hibi have proved a persistence theorem for exterior algebras. Green characterized Hilbert functions of rings when moding out by a general linear form in a ring with given Hilbert function. In this paper the theorems mentioned above are generalized to modules over the polynomial ring or the exterior algebra.
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 1182215
zbMATH Keywords: Hilbert functions
zbMATH Keywords: persistence theorem
zbMATH Keywords: polynomial ring
zbMATH Keywords: exterior algebra
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1182215