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.
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