A note on the symmetric powers of the standard representation of S n

David Savitt; Richard P. Stanley

doi:10.37236/1484

A note on the symmetric powers of the standard representation of S _n

David Savitt, Richard P. Stanley

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In 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 S_n is asymptotic to n²/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n²/2, for this dimension. In particular, for n ≥ 7, these characters do not span the full space of class functions on S_n.

Original language	English (US)
Pages (from-to)	1-8
Number of pages	8
Journal	Electronic Journal of Combinatorics
Volume	7
Issue number	1 R
DOIs	https://doi.org/10.37236/1484
State	Published - 2000
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/1484

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abstract = "In 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 Sn is asymptotic to n2/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n2/2, for this dimension. In particular, for n ≥ 7, these characters do not span the full space of class functions on Sn.",

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AB - In 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 Sn is asymptotic to n2/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n2/2, for this dimension. In particular, for n ≥ 7, these characters do not span the full space of class functions on Sn.

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A note on the symmetric powers of the standard representation of S _n

Abstract

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