A central limit theorem for the signatures of 2-bridge knots
Fuente:
arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866917430401433600 |
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| author | Baker, Cody Cohen, Moshe Dam, Henry Felber, Rebecca Madras, Neal Saha, Ritvik Thackrah, Daisy |
| author_facet | Baker, Cody Cohen, Moshe Dam, Henry Felber, Rebecca Madras, Neal Saha, Ritvik Thackrah, Daisy |
| contents | Cohen, Lowrance, Madras, and Raanes computed the average (absolute value of) signature over all 2-bridge knots with crossing number $c$ by introducing the number $s(c,σ)$ of 2-bridge knots of crossing number $c$ and signature $σ$. Here we provide a closed formula for this number. We use these calculations to show that the distribution of the signatures of 2-bridge knots with crossing number $c$ approaches a normal distribution as $c$ tends to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21107 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A central limit theorem for the signatures of 2-bridge knots Baker, Cody Cohen, Moshe Dam, Henry Felber, Rebecca Madras, Neal Saha, Ritvik Thackrah, Daisy Geometric Topology 57K10, 60F05, 05A10 Cohen, Lowrance, Madras, and Raanes computed the average (absolute value of) signature over all 2-bridge knots with crossing number $c$ by introducing the number $s(c,σ)$ of 2-bridge knots of crossing number $c$ and signature $σ$. Here we provide a closed formula for this number. We use these calculations to show that the distribution of the signatures of 2-bridge knots with crossing number $c$ approaches a normal distribution as $c$ tends to infinity. |
| title | A central limit theorem for the signatures of 2-bridge knots |
| topic | Geometric Topology 57K10, 60F05, 05A10 |
| url | https://arxiv.org/abs/2604.21107 |