The Enumeration of Alternating Pretzel Links

Charlotte Aspinwall; Tobias Clark; Yuanan Diao

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arXiv · 2412.06103

The Enumeration of Alternating Pretzel Links

Charlotte Aspinwall·Tobias Clark·Yuanan Diao

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Abstract

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 $c$.

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Charlotte Aspinwall, Tobias Clark, Yuanan Diao. 2024-12-08. The Enumeration of Alternating Pretzel Links. https://arxiv.org/abs/2412.06103

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