PRIME KNOTS WITH ARC INDEX UP TO 11 AND AN UPPER BOUND OF ARC INDEX FOR NON-ALTERNATING KNOTS
2010 ◽
Vol 19
(12)
◽
pp. 1655-1672
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Keyword(s):
Every knot can be embedded in the union of finitely many half planes with a common boundary line in such a way that the portion of the knot in each half plane is a properly embedded arc. The minimal number of such half planes is called the arc index of the knot. We have identified all prime knots with arc index up to 11. We also proved that the crossing number is an upperbound of arc index for non-alternating knots. As a result the arc index is determined for prime knots up to twelve crossings.
2011 ◽
Vol 20
(05)
◽
pp. 741-747
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2018 ◽
Vol 27
(08)
◽
pp. 1850044
Keyword(s):
2017 ◽
Vol 26
(14)
◽
pp. 1750100
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Keyword(s):
2005 ◽
Vol 14
(06)
◽
pp. 713-733
◽
2000 ◽
Vol 10
(01)
◽
pp. 73-78
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Keyword(s):
1986 ◽
Vol 104
(3-4)
◽
pp. 261-277
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Keyword(s):