Revision as of 16:17, 17 March 2019 edit BD2412 (talk \| contribs) Autopatrolled, Administrators 2,528,047 edits m →Symmetric polynomials: Fixing links to disambiguation pages, improving links, other minor cleanup tasks Tag: AWB ← Previous edit		Revision as of 03:00, 18 August 2019 edit undo Dgpop (talk \| contribs) Extended confirmed users 57,742 edits →Defining individual symmetric functions: WP:NOTED Next edit →
Line 47: === Defining individual symmetric functions === ~~It should be noted that the~~The name "symmetric function" for elements of Λ<sub>''R''</sub> is a [[misnomer]]: in neither construction the elements are functions, and in fact, unlike symmetric polynomials, no function of independent variables can be associated to such elements (for instance ''e''<sub>1</sub> would be the sum of all infinitely many variables, which is not defined unless restrictions are imposed on the variables). However the name is traditional and well established; it can be found both in (Macdonald, 1979), which says (footnote on p. 12) <blockquote>The elements of Λ (unlike those of Λ<sub>''n''</sub>) are no longer polynomials: they are formal infinite sums of monomials. We have therefore reverted to the older terminology of symmetric functions.</blockquote> (here Λ<sub>''n''</sub> denotes the ring of symmetric polynomials in ''n'' indeterminates), and also in (Stanley, 1999).

Ring of symmetric functions: Difference between revisions