Distinguishing Eleven Crossing Knots

Work has been done on the tabulation of knots since the last century. Perko [11] presents 552 distinct knots with eleven crossings and also provides a list of knot tabulations. In 1979 Richard Hartley drew our attention to Perko's work and to seven pairs of eleven crossing knots which Perko had not succeeded in distinguishing at that time. We indicate how we distinguished these pairs using group-theoretic calculations, not routinely applied by knot theorists. These knot pairs have now also been distinguished by Perko in the cited work and by Thistlethwaite (unpublished) using more usual calculations.