Papers › All Prime Knots Through 10 Crossings Have Superbridge Index ≤5
All Prime Knots Through 10 Crossings Have Superbridge Index ≤5
Clayton Shonkwiler
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This paper gives new upper bounds on the stick numbers of the knots 9₁₈, 10₁₈, 10₅₈, 10₆₆, 10₆₈, 10₈₀, 10₈₂, 10₈₄, 10₉₃, 10₁₀₀, and 10₁₅₂, as well as on the equilateral stick number of 10₇₉. These bounds imply that the knots 10₅₈, 10₆₆, and 10₈₀ have superbridge index ≤5, completing the project of showing that no prime knots through 10 crossings can have superbridge index larger than 5. The current best bounds on stick number and superbridge index for prime knots through 10 crossings are given in Appendix A.
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