Prime knots whose arc index is smaller than the crossing number
Geometric Topology
2011-06-15 v1
Abstract
It is known that the arc index of alternating knots is the minimal crossing number plus two and the arc index of prime nonalternating knots is less than or equal to the minimal crossing number. We study some cases when the arc index is strictly less than the minimal crossing number. We also give minimal grid diagrams of some prime nonalternating knots with 13 crossings and 14 crossings whose arc index is the minimal crossing number minus one.
Cite
@article{arxiv.1106.2723,
title = {Prime knots whose arc index is smaller than the crossing number},
author = {Gyo Taek Jin and Hwa Jeong Lee},
journal= {arXiv preprint arXiv:1106.2723},
year = {2011}
}
Comments
30 pages, 31 figures, 1 table and 379 minimal grid diagrams