Thresholds for patterns in random permutations with a given number of inversions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910562277916672 |
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| author | Bevan, David Threlfall, Dan |
| author_facet | Bevan, David Threlfall, Dan |
| contents | We explore how the asymptotic structure of a random permutation of $[n]$ with $m$ inversions evolves, as $m$ increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The threshold for the appearance of a classical pattern depends on the greatest number of inversions in any of its sum indecomposable components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01182 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Thresholds for patterns in random permutations with a given number of inversions Bevan, David Threlfall, Dan Combinatorics 05A05, 60C05 We explore how the asymptotic structure of a random permutation of $[n]$ with $m$ inversions evolves, as $m$ increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The threshold for the appearance of a classical pattern depends on the greatest number of inversions in any of its sum indecomposable components. |
| title | Thresholds for patterns in random permutations with a given number of inversions |
| topic | Combinatorics 05A05, 60C05 |
| url | https://arxiv.org/abs/2312.01182 |