The Enumeration of Alternating Pretzel Links
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915153689182208 |
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| author | Aspinwall, Charlotte Clark, Tobias Diao, Yuanan |
| author_facet | Aspinwall, Charlotte Clark, Tobias Diao, Yuanan |
| contents | In this paper, we tabulate the set of alternating pretzel links. Specifically, for any given crossing number $c$, we derive a closed formula that would allow us to compute $\mathcal{P}(c)$, the total number of alternating pretzel links with crossing number $c$. Numerical computation suggests that $\mathcal{P}(c)\approx 0.155e^{0.588c}$. That is, the number of alternating pretzel links with a given crossing number $c$ grows exponentially in terms of $c$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_06103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Enumeration of Alternating Pretzel Links Aspinwall, Charlotte Clark, Tobias Diao, Yuanan Geometric Topology (2020): Primary: 57K10, Secondary: 57K14 In this paper, we tabulate the set of alternating pretzel links. Specifically, for any given crossing number $c$, we derive a closed formula that would allow us to compute $\mathcal{P}(c)$, the total number of alternating pretzel links with crossing number $c$. Numerical computation suggests that $\mathcal{P}(c)\approx 0.155e^{0.588c}$. That is, the number of alternating pretzel links with a given crossing number $c$ grows exponentially in terms of $c$. |
| title | The Enumeration of Alternating Pretzel Links |
| topic | Geometric Topology (2020): Primary: 57K10, Secondary: 57K14 |
| url | https://arxiv.org/abs/2412.06103 |