Symmetric function: Difference between revisions

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

{{technical|date=March 2013}}

In [[mathematics]], a '''symmetric function of ''n'' variables''' is one whose value given n [[argument of a function|arguments]] is the same no matter the order of the arguments. SoFor example, if e.g. <math>f(\bold{x})=f(x_1,x_2,x_3)</math>, theis function can bea symmetric on all its variablesfunction, or just onthen <math>f(x_1,x_2)=f(x_2,x_1)</math>, for all pairs <math>(x_2x_1,x_3x_2)</math>, orin the ___domain of <math>(x_1,x_3)f</math>. While this notion can apply to any type of function whose ''n'' arguments have the same ___domain set, it is most often used for [[polynomial function]]s, in which case these are the functions given by [[symmetric polynomials]]. There is very little systematic theory of symmetric non-polynomial functions of ''n'' variables, so this sense is little-used, except as a general definition.

== Symmetrization ==