On the asymptotic enumeration and limit shapes of monotone grid classes of permutations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915367223296000 |
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| author | Alshammari, Noura Bevan, David |
| author_facet | Alshammari, Noura Bevan, David |
| contents | We exhibit a procedure to asymptotically enumerate monotone grid classes of permutations. This is then applied to compute the asymptotic number of permutations in any connected one-corner class. Our strategy consists of enumerating the gridded permutations, finding the asymptotic distribution of points between the cells in a typical large gridded permutation, and analysing in detail the ways in which a typical permutation can be gridded. We also determine the limit shape of any connected monotone grid class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the asymptotic enumeration and limit shapes of monotone grid classes of permutations Alshammari, Noura Bevan, David Combinatorics 05A05, 05A16 We exhibit a procedure to asymptotically enumerate monotone grid classes of permutations. This is then applied to compute the asymptotic number of permutations in any connected one-corner class. Our strategy consists of enumerating the gridded permutations, finding the asymptotic distribution of points between the cells in a typical large gridded permutation, and analysing in detail the ways in which a typical permutation can be gridded. We also determine the limit shape of any connected monotone grid class. |
| title | On the asymptotic enumeration and limit shapes of monotone grid classes of permutations |
| topic | Combinatorics 05A05, 05A16 |
| url | https://arxiv.org/abs/2408.00607 |