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Moshe Cohen and
Adam M. Lowrance
The average genus of a 2-bridge knot is asymptotically linear
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| Published: |
July 22, 2024. |
| Keywords: |
knot, genus, 2-bridge, rational knot. |
| Subject [2020]: |
57K10, 05A19. |
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Abstract
Experimental work suggests that the Seifert genus of a knot grows linearly with respect to the crossing number of the knot. In this article, we use a billiard table model for 2-bridge or rational knots to show that the average genus of a 2-bridge knot with crossing number c asymptotically approaches c/4+1/12.
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| Acknowledgements
The second author was supported by NSF grant DMS-1811344.
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| Author information
Moshe Cohen
Mathematics Department
State University of New York at New Paltz
New Paltz, NY 12561, USA
cohenm@newpaltz.edu
Adam M. Lowrance
Department of Mathematics and Statistics
Vassar College
Poughkeepsie, NY 12604, USA
adlowrance@vassar.edu
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