Editing Ring of symmetric functions (section)

{{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 [[ring (mathematics)|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]].

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