## 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 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 ≥ 7, these characters do not span the full space of class functions on S_{n}.

Original language | English (US) |
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Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Electronic Journal of Combinatorics |

Volume | 7 |

Issue number | 1 R |

DOIs | |

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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