Universal knot diagrams-Reference-Cited by-同舟云学术

Universal knot diagrams

Published:2019-06 Issue:07 Volume:28 Page:1950031
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Even-Zohar Chaim¹,Hass Joel¹,Linial Nati²,Nowik Tahl³

Affiliation:

1. Mathematics Department, University of California at Davis, Davis, CA, USA

2. Department of Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel

3. Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216519500317

Reference35 articles.

1. Knot projections with a single multi-crossing

2. Bounds on übercrossing and petal numbers for knots

3. Volume and determinant densities of hyperbolic rational links

4. A Lemma on Systems of Knotted Curves

5. Theory of Braids

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