Knot mosaic tabulation

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.