16 citations · 28 across the 10 of their papers we have counts for
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math.GT2010★ 1 cited
Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots
Scott M. Garrabrant, Jim Hoste, Patrick D. Shanahan
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 suffi…
math.GT2010★ 16 cited
Epimorphisms and Boundary Slopes of 2-Bridge Knots
Jim Hoste, Patrick D. Shanahan
In this article we study a partial ordering on knots in the 3-sphere where K_1 is greater than or equal to K_2 if there is an epimorphism from the knot group of K_1 onto the knot g…