The distribution of genera of 2-bridge knots
Volume 267 / 2024
Fundamenta Mathematicae 267 (2024), 195-229
MSC: Primary 57K10
DOI: 10.4064/fm230719-2-10
Published online: 20 November 2024
Abstract
The average genus of a 2-bridge knot with crossing number $c$ approaches ${c}/{4} + {1}/{12}$ as $c$ approaches infinity, as proven by Suzuki and Tran and independently by 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 ${c}/{16}-{17}/{144}$ as $c$ approaches infinity. We prove that the distribution of genera of 2-bridge knots is asymptotically normal.
