The study of knot mosaics is based upon representing knot diagrams using a set of tiles on a square grid. This relatively new branch of knot theory has many unanswered questions, especially regarding the efficiency with which we draw knots as mosaics. While any knot or link can be displayed as a mosaic, it is still unknown how large the mosaic needs to be, and how many tiles are needed for every knot. In this paper we implement an algorithmic programming approach to find the tile and mosaic number of all knots with crossing number 10 and less. We also introduce an online tool in which users can search, create, and identify knot mosaics.


Sponsored by Aaron Heap and Doug Baldwin

Canning— Appendix A.pdf (342 kB)
Mosaics from theorem 4.2