Space-Efficient Knot Mosaics for Prime Knots with Mosaic Number 6
Abstract
In 2008, Kauffman and Lomonaco introduce the concepts of a knot mosaic and the mosaic number of a knot or link, the smallest integer such that a knot or link can be represented on an -mosaic. In arXiv:1702.06462, the authors explore space-efficient knot mosaics and the tile number of a knot or link, the smallest number of non-blank tiles necessary to depict the knot or link on a mosaic. They determine bounds for the tile number in terms of the mosaic number. In this paper, we focus specifically on prime knots with mosaic number 6. We determine a complete list of these knots, provide a minimal, space-efficient knot mosaic for each of them, and determine the tile number (or minimal mosaic tile number) of each of them.
Cite
@article{arxiv.1803.08004,
title = {Space-Efficient Knot Mosaics for Prime Knots with Mosaic Number 6},
author = {Aaron Heap and Douglas Knowles},
journal= {arXiv preprint arXiv:1803.08004},
year = {2020}
}
Comments
Portions of this article previously appeared as arXiv:1702.06462, which was split in two during refereeing