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.

Author Bio

I recall my mother telling me that she would walk by immense buildings for years on her way to work, but she never realized that it was going to be the university I would be attending. Now only a semester away from my Bachelors of Science in Mathematics, I look forward to attending graduate school and pursuing a degree in Forensic Science. As a young child I was deeply involved in my studies. While in high school, I was included in the Who's Who Amongst American High School Students, an institution who seeks to introduce America to students who excel in academia. As a college student I continued to receive highly credited awards, such as the National Dean's List, and became a part of the National Scholars Honor Society. Throughout my academic career I have continued my volunteering services in places like Precious Blood Church, Juvenile Diabetes Research Foundation and others, as means of supporting my community and being a role model for young adults and my family. Coming from a traditional home, I took extra precaution when agreeing to be a part of the Research Experiences for Undergraduates (REU) program as it was out of state. Nonetheless, the research was extremely intense and very well worth it as it was one of the greatest experiences I have had thus far.