Constructions of and Bounds on the Toric Mosaic Number
Geometric Topology
2025-11-06 v1
Abstract
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.
Cite
@article{arxiv.2504.02265,
title = {Constructions of and Bounds on the Toric Mosaic Number},
author = {Kendall Heiney and Margaret Kipe and Samantha Pezzimenti and Kaelyn Pontes and Luc Ta},
journal= {arXiv preprint arXiv:2504.02265},
year = {2025}
}
Comments
21 pages, 11 figures