The petal-number bound for torus knots

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Let rr and ss be relatively prime integers with 1<r<s1 < r < s, and let Tr,sT_{r,s} denote the corresponding torus knot. The petal-number bound for torus knots.

p(Tr,s)≤2s−2⌊sr⌋+1.p(T_{r,s})\leq 2s-2\Big\lfloor \frac{s}{r} \Big\rfloor+1.

The authors are led to this conjecture by the cases established earlier in the paper, including r=2r=2 and the condition of their main theorem; its status is not resolved in the supplied source.

References

Primary source

Hyoungjun Kim, Sungjong No and Hyungkee Yoo, “Petal number of torus knots using superbridge indices”, arXiv:2209.14702 (2022).

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