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

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

Geometric Topology 2026-04-24 v1

Authors: Cody Baker , Moshe Cohen , Henry Dam , Rebecca Felber , Neal Madras , Ritvik Saha , Daisy Thackrah

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.

Keywords

signature 2-bridge knot central limit theorem crossing number normal distribution

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@article{arxiv.2604.21107,
  title  = {A central limit theorem for the signatures of 2-bridge knots},
  author = {Cody Baker and Moshe Cohen and Henry Dam and Rebecca Felber and Neal Madras and Ritvik Saha and Daisy Thackrah},
  journal= {arXiv preprint arXiv:2604.21107},
  year   = {2026}
}

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15 pages, 1 figure, 2 tables

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

Abstract

Keywords

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