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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.00343 |
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| _version_ | 1866908571466203136 |
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| author | Clay, Alexander |
| author_facet | Clay, Alexander |
| contents | We prove central limit theorems for the number of descents and the number of inversions after a shelf-shuffle. In particular, we bound the convergence rate for the number of inversions independently of the number of shelves. Along the way, we determine the mean and variance for the number of inversions after a shelf shuffle, which was also an open problem. We also suggest ways to extend our results to biased shelf-shuffles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit Theorems for Descents and Inversions of Shelf-Shuffles Clay, Alexander Probability Combinatorics We prove central limit theorems for the number of descents and the number of inversions after a shelf-shuffle. In particular, we bound the convergence rate for the number of inversions independently of the number of shelves. Along the way, we determine the mean and variance for the number of inversions after a shelf shuffle, which was also an open problem. We also suggest ways to extend our results to biased shelf-shuffles. |
| title | Limit Theorems for Descents and Inversions of Shelf-Shuffles |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2510.00343 |