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.
Original language | English |
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Article number | 1950031 |
Journal | Journal of Knot Theory and its Ramifications |
Volume | 28 |
Issue number | 7 |
DOIs | |
State | Published - 1 Jun 2019 |
Bibliographical note
Publisher Copyright:© 2019 World Scientific Publishing Company.
Funding
at HUJI, supported by ERC 339096. Work of J. Hass was also supported by NSF grant DMS-1758107. This work was supported by BSF Grant 2012188. The numerical experiments were carried out with the facilities of the School of Computer Science and Engineering at HUJI, supported by ERC 339096. Work of J. Hass was also supported by NSF grant DMS-1758107. This work was supported by BSF Grant 2012188. The numerical experiments were carried out with the facilities of the School of Computer Science and Engineering
Funders | Funder number |
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ERC 339096 | 339096 |
Bloom's Syndrome Foundation | 2012188 |
National Sleep Foundation | DMS-1758107 |
Keywords
- Potholder
- meander
- one-pure braids