UPPER BOUNDS IN THE OHTSUKI–RILEY–SAKUMA PARTIAL ORDER ON 2-BRIDGE KNOTS
2012 ◽
Vol 21
(09)
◽
pp. 1250084
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Keyword(s):
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K1 we characterize all other 2-bridge knots K2 such that {K1, K2} has an upper bound. As an application we answer a question of Suzuki, showing that there is no upper bound for the set consisting of the trefoil and figure-eight knots.
1978 ◽
Vol 25
(2)
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pp. 241-249
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1959 ◽
Vol 11
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pp. 440-451
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2021 ◽
Vol 14
(1)
◽
pp. 314-326
1986 ◽
Vol 23
(04)
◽
pp. 851-858
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