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Universal Knot Diagrams

26 Apr 2018arXiv:1804.09860links table onlyarchive 2025-07-28

Chaim Even-Zohar, Joel Hass, Nati Linial, Tahl Nowik

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We study collections of planar curves that yield diagrams for all knots. In particular, we show that a very special class called potholder curves carries all knots. This has implications for realizing all knots and links as special types of meanders and braids. We also introduce and apply a method to compare the efficiency of various classes of curves that represent all knots.

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