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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 \cite{Jin2006} and \cite{Jin2011} 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~\cite{Jin2020}.
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참고문헌 (9)
참고문헌 신청
Peter R. Cromwell / 1995 / Embedding knots and links in an open book I: Basic properties / Topology and its Applications 64(1):37~58
Peter R. Cromwell / 1996 / Embedding knots and links in an open book II. Bounds on arc index / Mathematical Proceedings of the Cambridge Philosophical Society 119(2):309~319
J. Hoste / Knotscape
Jim Hoste / 1998 / The first 1,701,936 knots / The Mathematical Intelligencer 20(4):33~48
G. T. Jin / 2006 / Intelligence of low dimensional topology / World Sci. Publ :65~74
Peter R. Cromwell / 1996 / Embedding knots and links in an open book II. Bounds on arc index / Mathematical Proceedings of the Cambridge Philosophical Society 119(2):309~319
J. Hoste / Knotscape
Jim Hoste / 1998 / The first 1,701,936 knots / The Mathematical Intelligencer 20(4):33~48
G. T. Jin / 2006 / Intelligence of low dimensional topology / World Sci. Publ :65~74
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