We extend mosaic knot theory to virtual knots and define a new type of knot: virtual mosaic knot. As in classical knots, Reidemeister moves are applied to a virtual mosaic knot to transform one knot diagram into another. Additionally, given the mosaic number of a virtual knot, we find an upper bound on the sum of the classical and virtual crossing numbers. Furthermore, given the classical and virtual crossing numbers of a knot, we find a lower bound on the virtual mosaic number of a knot.
J. Alan Alewine, Department of Mathematics, McKendree University firstname.lastname@example.org
Garduno, Irina T.
"Virtual Mosaic Knots,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 10
, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol10/iss2/5