A central limit theorem for the signatures of 2-bridge knots

Cody Baker; Moshe Cohen; Henry Dam; Rebecca Felber; Neal Madras; Ritvik Saha; Daisy Thackrah

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arXiv · 2604.21107

A central limit theorem for the signatures of 2-bridge knots

Cody Baker·Moshe Cohen·Henry Dam·Rebecca Felber·Neal Madras·Ritvik Saha·Daisy Thackrah

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Abstract

Cohen, Lowrance, Madras, and Raanes computed the average (absolute value of) signature over all 2-bridge knots with crossing number $c$ by introducing the number $s(c,\sigma)$ of 2-bridge knots of crossing number $c$ and signature $\sigma$. Here we provide a closed formula for this number. We use these calculations to show that the distribution of the signatures of 2-bridge knots with crossing number $c$ approaches a normal distribution as $c$ tends to infinity.

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Cody Baker, Moshe Cohen, Henry Dam, Rebecca Felber, Neal Madras, Ritvik Saha, Daisy Thackrah. 2026-04-22. A central limit theorem for the signatures of 2-bridge knots. https://arxiv.org/abs/2604.21107

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