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Knot mosaic
tabulation
Hwa Jeong Lee, Lewis D. Ludwig, Joseph Paat and Amanda Peiffer
Vol. 11 (2018), No. 1, 13–26
DOI: 10.2140/involve.2018.11.13
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Abstract |
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In 2008, Lomonaco and Kauffman introduced a knot mosaic system to define a quantum knot system. A quantum knot is used to describe a physical quantum system such as the topology or status of vortexing that occurs in liquid helium II for example. Kuriya and Shehab proved that knot mosaic type is a complete invariant of tame knots. In this article, we consider the mosaic number of a knot, which is a natural and fundamental knot invariant defined in the knot mosaic system. We determine the mosaic number for all eight-crossing or fewer prime knots. This work is written at an introductory level to encourage other undergraduates to understand and explore this topic. No prior knowledge of knot theory is assumed or required. |
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Keywords
knots, knot mosaic, mosaic number, crossing number
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Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27
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Milestones
Received: 14 October 2015
Revised: 21 October 2016
Accepted: 2 November 2016
Published: 17 July 2017
Communicated by Kenneth S. Berenhaut
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Authors |
| Hwa Jeong Lee | |
| School of Undergraduate Studies,
College of Transdisciplinary Studies Daegu Gyeongbuk Institute of Science and Technology Daegu 42988 South Korea |
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| Lewis D. Ludwig | |
| Department of Mathematics and
Computer Science Denison University 100 West College Granville, OH 43023 United States |
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| Joseph Paat | |
| Department of Applied Mathematics
and Statistics Johns Hopkins 211-E Whitehead Hall 3400 N. Charles St. Baltimore, MD 21218-2682 United States |
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| Amanda Peiffer | |
| Department of Math and Computer
Science Denison University Granville, OH 43020 United States |
Program in Chemical Biology University of Michigan 930 N University Ave. Ann Arbor, MI 48109 United States |
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