Mosaic knot theory is a young and exciting area of mathematics. Since it is still in its mathematical infancy, there are many basic questions still unanswered. The main goal of the field is to represent knots on a square grid using a certain set of tiles. From those tiles we can build knot projections. The smallest n × n grid that each knot with crossing number 10 or less can fit on is unknown. In this paper, we explain how we developed a program that creates and identifies every knot on a 7 × 7 mosaic, and we find every knot with crossing number 10 or less that can fit on a 7-mosaic with tile number 27 or 29.
"Space-Efficient Knot Mosaics of Size 7,"
Proceedings of GREAT Day: Vol. 2019
, Article 13.
Available at: https://knightscholar.geneseo.edu/proceedings-of-great-day/vol2019/iss1/13