The distribution of genera of 2-bridge knots
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909738142269440 |
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| author | Cohen, Moshe DiNardo, Abigail Lowrance, Adam M. Raanes, Steven Rivera, Izabella M. Steindl, Andrew J. Wanebo, Ella S. |
| author_facet | Cohen, Moshe DiNardo, Abigail Lowrance, Adam M. Raanes, Steven Rivera, Izabella M. Steindl, Andrew J. Wanebo, Ella S. |
| contents | The average genus of a 2-bridge knot with crossing number $c$ approaches $\frac{c}{4} + \frac{1}{12}$ as $c$ approaches infinity, as proven by Suzuki and Tran and independently Cohen and Lowrance. In this paper, for the genera of $2$-bridge knots of a fixed crossing number $c$, we show that the median and mode are both $\lfloor \frac{c+2}{4} \rfloor$ and that the variance approaches $\frac{c}{16}-\frac{17}{144}$ as $c$ approaches infinity. We prove that the distribution of genera of 2-bridge knots is asymptotically normal. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_09399 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The distribution of genera of 2-bridge knots Cohen, Moshe DiNardo, Abigail Lowrance, Adam M. Raanes, Steven Rivera, Izabella M. Steindl, Andrew J. Wanebo, Ella S. Geometric Topology 57K10 The average genus of a 2-bridge knot with crossing number $c$ approaches $\frac{c}{4} + \frac{1}{12}$ as $c$ approaches infinity, as proven by Suzuki and Tran and independently Cohen and Lowrance. In this paper, for the genera of $2$-bridge knots of a fixed crossing number $c$, we show that the median and mode are both $\lfloor \frac{c+2}{4} \rfloor$ and that the variance approaches $\frac{c}{16}-\frac{17}{144}$ as $c$ approaches infinity. We prove that the distribution of genera of 2-bridge knots is asymptotically normal. |
| title | The distribution of genera of 2-bridge knots |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2307.09399 |