Journal of the
Korean Mathematical Society JKMS

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}.

Keywords: Knot, arc presentation, arc index, Cromwell matrix, grid diagram

MSC numbers: 57M25

Supported by: This work was supported in part by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2013-056086). This work was accelerated by the parallel computing service of KISTI Supercomputing Center.