The Enumeration of Alternating Pretzel Links
Charlotte Aspinwall, Tobias Clark, Yuanan Diao

TL;DR
This paper provides a closed-form formula for counting alternating pretzel links with a given crossing number, revealing exponential growth in their enumeration as crossing number increases.
Contribution
It introduces a closed formula for enumerating alternating pretzel links based on crossing number, advancing understanding of their combinatorial complexity.
Findings
Number of alternating pretzel links grows exponentially with crossing number.
Derived a closed formula for counting these links.
Numerical estimates suggest exponential growth rate.
Abstract
In this paper, we tabulate the set of alternating pretzel links. Specifically, for any given crossing number , we derive a closed formula that would allow us to compute , the total number of alternating pretzel links with crossing number . Numerical computation suggests that . That is, the number of alternating pretzel links with a given crossing number grows exponentially in terms of .
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Taxonomy
TopicsGraph theory and applications · Advanced Topics in Algebra · Algebraic structures and combinatorial models
