The distribution of genera of 2-bridge knots
Autor: | Cohen, Moshe, DiNardo, Abigail, Lowrance, Adam M., Raanes, Steven, Rivera, Izabella M., Steindl, Andrew J., Wanebo, Ella S. |
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Rok vydání: | 2023 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: 23 pages, 4 figures |
Databáze: | arXiv |
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