References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

A minimal set of generators for the ring of multisymmetric functionsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2007 (English)In: Annales de l'Institut Fourier, ISSN 0373-0956, Vol. 57, no 6, 1741-1769 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2007. Vol. 57, no 6, 1741-1769 p.
##### Keyword [en]

symmetric functions, generators, divided powers, vector invariants
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-37132ISI: 000252868000001ScopusID: 2-s2.0-38349187610OAI: oai:DiVA.org:kth-37132DiVA: diva2:432189
#####

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#####

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#####

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Available from: 2011-08-01 Created: 2011-08-01 Last updated: 2011-08-01Bibliographically approved

The purpose of this article is to give, for any (commutative) ring A, an explicit minimal set of generators for the ring of multisymmetric functions TSAd[x(1),...,x(r)]) = (A[x(1),...,x(r)](circle times)A(d))8(d) A as an A-algebra. In characteristic zero, i.e. when A is a Q-algebra, a minimal set of generators has been known since the 19(th) century. A rather si-nall generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound oil the generators, improving the degree bound previously obtained by Fleischmann. As Gamma(d)(A) (A[x(1),...,x(r)]) = TSAd (A[x(1),...,x(r)]) we also obtain generators for di A vided powers algebras: If B is a finitely generated A-algebra with a given surjection A[x(1), x(2),...,x(r)] --> B then using the corresponding surjection Gamma(d)(A) (A[x(1),...,x(r)]) --> Gamma(d)(A) (B) we get generators for Gamma(d)(A) (B).

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});