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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.11061 |
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| _version_ | 1866917268375470080 |
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| author | Kagey, Peter Mawhinney, Kai |
| author_facet | Kagey, Peter Mawhinney, Kai |
| contents | We construct a statistic-swapping involution on the Cartesian product of the generalized symmetric group $S(k,n)$ with the symmetric group $S_{kn}$, which swaps the number of fixed points in the generalized symmetric group element with the number of $k$-cycles in the symmetric group element. This gives a combinatorial proof for a probabilistic observation: the distribution of fixed points on $S(k,n)$ matches the distribution of $k$-cycles on $S_{kn}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A statistic-swapping involution on the Cartesian product of the symmetric group $S_{kn}$ and the generalized symmetric group $S(k,n)$ Kagey, Peter Mawhinney, Kai Combinatorics 05A19 We construct a statistic-swapping involution on the Cartesian product of the generalized symmetric group $S(k,n)$ with the symmetric group $S_{kn}$, which swaps the number of fixed points in the generalized symmetric group element with the number of $k$-cycles in the symmetric group element. This gives a combinatorial proof for a probabilistic observation: the distribution of fixed points on $S(k,n)$ matches the distribution of $k$-cycles on $S_{kn}$. |
| title | A statistic-swapping involution on the Cartesian product of the symmetric group $S_{kn}$ and the generalized symmetric group $S(k,n)$ |
| topic | Combinatorics 05A19 |
| url | https://arxiv.org/abs/2602.11061 |