PRIME KNOTS WHOSE ARC INDEX IS SMALLER THAN THE CROSSING NUMBER

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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.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2012-09
Language
English
Article Type
Article
Keywords

EMBEDDING KNOTS; OPEN-BOOK; LINKS

Citation

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.21, no.10

ISSN
0218-2165
DOI
10.1142/S0218216512501039
URI
http://hdl.handle.net/10203/104272
Appears in Collection
MA-Journal Papers(저널논문)
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