Prime knots whose arc index is smaller than the crossing number

Details Prime knots whose arc index is smaller than the crossing number Prime knots whose arc index is smaller than the crossing number

2011-06-13

arxiv.org/abs/1106.2723v1

Mathematics

Geometric Topology

30 pages, 31 figures, 1 table and 379 minimal grid diagrams

Scientific paper

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.

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