symmetric function

Function that is invariant under all permutations of its variables

EntityQ981351

Subclass of: function
Part of: ring of symmetric functions

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a function of variables is symmetric if its value is the same no matter the order of its arguments. For example, a function of two arguments is a symmetric function if and only if for all and such that and are in the domain of The most commonly encountered symmetric functions are polynomial functions, which are given by the symmetric polynomials.

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16 statements · 25% with external sources · numbers in brackets are citations

Defining formula: \forall x_1, \dots, x_n B(x_{\sigma(1)}, \ldots, x_{\sigma(n)})=B(x_1, \ldots, x_n)
Has characteristic: symmetry
Different from: symmetric operator

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12 identifiers linking symmetric function across the web's reference databases

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Source last edited September 6, 2026. AIDB refreshes this page daily.

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AIDB. (2026). symmetric function (Q981351). Retrieved from https://aidb.si/e/symmetric-function-Q981351