A New Shape to the RUG : Further Exploration of the Region Unknotting Game

Abstract

A region crossing change is an unknotting operation on a knot diagram. In the past, knot games have been used to demonstrate and discover properties of families of knots. We will find winning strategies of knot games to explore the effects of region crossing changes on twist and torus knot diagrams. Furthermore, we will focus on exploring the effects of changing the rules of the Region Unknotting Game, primarily on twist knots with an even number of crossings.