Ring of symmetric functions: Difference between revisions

Revision as of 12:31, 5 May 2014

Revision as of 08:16, 30 October 2014

Line 1:

{{About|the ring of symmetric functions in algebraic combinatorics|general properties of symmetric functions|symmetric function}}

In [[algebra]] and in particular in [[algebraic combinatorics]], the '''ring of symmetric functions''', is a specific limit of the rings of [[symmetric polynomial]]s in ''n'' indeterminates, as ''n'' goes to infinity. This ring serves as universal structure in which relations between symmetric polynomials can be expressed in a way independent of the number ''n'' of indeterminates (but its elements are neither polynomials nor functions). Among other things, this ring plays an important role in the [[representation theory of the symmetric group]]s.

The ring of symmetric functions can be given a coproduct and a bilinear form making it into a positive selfadjoint graded [[Hopf algebra]] that is both commutative and cocommutative.