Polynomial Expressions for Symmetric Group Characters on Cycles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908783286943744 |
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| author | Moshaiov, Tom Zemel, Shaul |
| author_facet | Moshaiov, Tom Zemel, Shaul |
| contents | In \cite{[CZ]}, Cohen and Zemel showed that for a partition $λ\vdash k$, the dimension of the irreducible representation of $S_{n}$ corresponding to the partition $(n-k,λ) \vdash n$ is a polynomial of degree $k$ in $n$, whose coefficients in the binomial basis count standard Young tableaux of shape $λ$ with special restrictions. In this paper, we generalize their results on the representation's dimension to character values on arbitrary cycles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_16360 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomial Expressions for Symmetric Group Characters on Cycles Moshaiov, Tom Zemel, Shaul Combinatorics 05A17, 05A19, 20C30, 05E10 In \cite{[CZ]}, Cohen and Zemel showed that for a partition $λ\vdash k$, the dimension of the irreducible representation of $S_{n}$ corresponding to the partition $(n-k,λ) \vdash n$ is a polynomial of degree $k$ in $n$, whose coefficients in the binomial basis count standard Young tableaux of shape $λ$ with special restrictions. In this paper, we generalize their results on the representation's dimension to character values on arbitrary cycles. |
| title | Polynomial Expressions for Symmetric Group Characters on Cycles |
| topic | Combinatorics 05A17, 05A19, 20C30, 05E10 |
| url | https://arxiv.org/abs/2601.16360 |