Mirror-Curves and Knot Mosaics
Abstract
Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot mosaics [23], mirror-curves, and grid diagrams [3,7,22,24]. Hence, we introduce codes for mirror-curves treated as knot or link diagrams placed in rectangular square grids, suitable for software implementation. We provide tables of minimal mirror-curve codes for knots and links obtained from rectangular grids of size 3x3 and px2 (p<5), and describe an efficient algorithm for computing the Kauffman bracket and L-polynomials [18,19,20] directly from mirror-curve representations.
Keywords
Cite
@article{arxiv.1106.3784,
title = {Mirror-Curves and Knot Mosaics},
author = {Slavik V. Jablan and Ljiljana Radovic and Radmila Sazdanovic and Ana Zekovic},
journal= {arXiv preprint arXiv:1106.3784},
year = {2011}
}