2025/04/03 by Heiney, Kendall, Kipe, Margaret, Pezzimenti, Samantha +2
#57K10 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2504.02265
Knot mosaics were introduced by Kauffman and Lomonaco in the context of quantum knots, but have since been studied for their own right. A classical knot mosaic is formed on a square grid. In this work, we identify opposite edges of the square to form mosaics on the surface of a torus. We provide two algorithms for efficiently constructing toric mosaics of torus knots, providing upper bounds for the toric mosaic number. Using these results and a computer search, we provide a census of known toric mosaic numbers.