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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.04054 |
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Table of Contents:
- The covering number of a non-linear character $χ$ of a finite group $G$ is the least positive integer $k$ such that every irreducible character of $G$ occurs in $χ^k$. We determine the covering numbers of irreducible characters of the symmetric group $S_n$ indexed by certain two-row partitions (and their conjugates), namely $(n-2,2)$ and $((n+1)/2, (n-1)/2)$ when $n$ is odd. We also determine the covering numbers of irreducible characters indexed by certain hook-partitions (and their conjugates), namely $(n-2,1^2)$, the almost self-conjugate hooks $(n/2+1, 1^{n/2-1})$ when $n$ is even, and the self-conjugate hooks $((n+1)/2, 1^{(n-1)/2})$ when $n$ is odd.