Symmetric function: Difference between revisions

Revision as of 09:10, 22 July 2021

Revision as of 22:31, 26 July 2021

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:By definition, a symmetric function with ''n'' variables has the property that

::<math>f(x_1,x_2,...,x_n) = f(x_2,x_1,...,x_n) = f(x_3,x_1,...,x_n,x_{n-1})</math> etc.

:In general, the function remains the same for every [[permutation]] of its variables. This means that, in this case,

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*[[Symmetrization]]

*[[Elementary symmetric polynomial]]

*[[Alternating polynomial|Alternating polynomials]]s

*[[Vandermonde polynomial]]

* [[Quasisymmetric function]]

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==References==

{{Reflist}}

* [[F. N. David]], [[M. G. Kendall]] & D. E. Barton (1966) ''Symmetric Function and Allied Tables'', [[Cambridge University Press]].

* Joseph P. S. Kung, [[Gian-Carlo Rota]], & [[Catherine Yan|Catherine H. Yan]] (2009) ''[[Combinatorics: The Rota Way]]'', §5.1 Symmetric functions, pp 222–5, Cambridge University Press, {{isbn|978-0-521-73794-4}} .