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In this paper we use continued fractions to study a partial order on the setof 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. Weestablish necessary and sufficient conditions for any set of 2-bridge knots tohave an upper bound with respect to the partial order. Moreover, given any2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} hasan upper bound. As an application we answer a question of Suzuki, showing thatthere is no upper bound for the set consisting of the trefoil and figure-eightknots.

UPPER BOUNDS IN THE OHTSUKI–RILEY–SAKUMA PARTIAL ORDER ON 2-BRIDGE KNOTS