A Note on the Symmetric Powers of the Standard Representation of S_n

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dc.creatorSavitt, David
dc.creatorStanley, Richard P.
dc.date2000-02-14
dc.date.accessioned2026-07-07T04:33:51Z
dc.date.available2026-07-07T04:33:51Z
dc.descriptionIn this paper, we prove that the dimension of the space spanned by the characters of the symmetric powers of the standard n-dimensional representation of the symmetric group S_n is asymptotic to n^2/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n^2/2, for this dimension. In particular, for n>6, these characters do not span the full space of class functions on S_n.
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/math/0002106
dc.identifierhttp://arxiv.org/abs/math/0002106
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58682
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject05E10
dc.titleA Note on the Symmetric Powers of the Standard Representation of S_n
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