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.
Rok vydání:	2023
Předmět:	Mathematics - Geometric Topology 57K10
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
Externí odkaz:	http://arxiv.org/abs/2307.09399 Zobrazit plný text záznamu View this record from Arxiv