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http://dx.doi.org/10.4134/JKMS.j200397

PRIME KNOTS WITH ARC INDEX 12 UP TO 16 CROSSINGS

Jin, Gyo Taek (Department of Mathematical Sciences Korea Advanced Institute of Science and Technology)
Kim, Hyuntae (Department of Mathematical Sciences Korea Advanced Institute of Science and Technology)
Lee, Seungwoo (Moasys Corporation)
Myung, Hun Joo (Korea Institute of Science and Technology Information)

Publication Information

Journal of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 967-976 More about this Journal

Abstract

We obtain the list of prime knots with arc index 12 up to 16 crossings and their minimal grid diagrams. This is a continuation of the works [5] and [8] in which Cromwell matrices were generated to obtain minimal grid diagrams of all prime knots up to arc index 11. We provide minimal grid diagrams of the prime alternating knots with arc index 12. They are the 10 crossing prime alternating knots. The full list of 19,513 prime knots of arc index 12 up to 16 crossings and their minimal grid diagrams can be found in the arXiv [6].

Keywords

Knot; arc presentation; arc index; Cromwell matrix; grid diagram;

Citations & Related Records

Reference

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