Counting pairs of cycles whose product is a permutation with restricted cycle lengths
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912084854308864 |
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| author | Bona, Miklos Pittel, Boris |
| author_facet | Bona, Miklos Pittel, Boris |
| contents | We find exact and asymptotic formulas for the number of pairs $(p,q)$ of $N$-cycles such that the all cycles of the product $p\cdot q$ have lengths from a given integer set. We then apply these results to prove a surprisingly high lower bound for the number of permutations whose block transposition distance from the identity is at least $(n+1)/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10024 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting pairs of cycles whose product is a permutation with restricted cycle lengths Bona, Miklos Pittel, Boris Combinatorics 05E10, 60C05 We find exact and asymptotic formulas for the number of pairs $(p,q)$ of $N$-cycles such that the all cycles of the product $p\cdot q$ have lengths from a given integer set. We then apply these results to prove a surprisingly high lower bound for the number of permutations whose block transposition distance from the identity is at least $(n+1)/2$. |
| title | Counting pairs of cycles whose product is a permutation with restricted cycle lengths |
| topic | Combinatorics 05E10, 60C05 |
| url | https://arxiv.org/abs/2407.10024 |