Vol. 11, No. 1, 2018

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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
Abstract

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.

Keywords
knots, knot mosaic, mosaic number, crossing number
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27
Milestones
Received: 14 October 2015
Revised: 21 October 2016
Accepted: 2 November 2016
Published: 17 July 2017

Communicated by Kenneth S. Berenhaut
Authors
Hwa Jeong Lee
School of Undergraduate Studies, College of Transdisciplinary Studies
Daegu Gyeongbuk Institute of Science and Technology
Daegu 42988
South Korea
Lewis D. Ludwig
Department of Mathematics and Computer Science
Denison University
100 West College
Granville, OH 43023
United States
Joseph Paat
Department of Applied Mathematics and Statistics
Johns Hopkins
211-E Whitehead Hall
3400 N. Charles St.
Baltimore, MD 21218-2682
United States
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