TL;DR
This paper demonstrates that potholder curves, a special class of planar curves, can represent all knots, and introduces methods to compare the efficiency of different knot-representing classes.
Contribution
It proves that potholder curves can realize all knots and links, and develops a framework to compare the efficiency of various knot diagram classes.
Findings
Potholder curves can represent all knots and links.
A method to compare the efficiency of different knot diagram classes.
Implications for realizing knots as meanders and braids.
Abstract
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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