Physical Sciences and Mathematics Commons^™

Enhancement On Counting Invariant On Symmetric Virtual Biracks, Melinda Ho

Scripps Senior Theses

This thesis introduces a new enhancement for virtual birack counting invariants. We first introduce knots and other general types of knots (oriented knots, framed knots, racks, and biracks). Then we’ll discuss the methods, knot invariants, mathematicians use to identify whether two knots are different. Next we’ll look at knots with virtual crossings and knots with a good involution. Finally, we introduce a new symmetric enhancement for virtual birack counting invariants and provide an example.