Ribbonlength of twisted torus knots

Abstract

The ribbonlength Rib(K) of a knot K is the infimum of the ratio of the length of any flat knotted ribbon with core K to its width. A twisted torus knot T p,q;r,s is obtained from the torus knot T p,q by twisting r adjacent strands s full twists. In this paper, we show that the ribbonlength of T p,q;r,s is less then or equal to 2(max{p, q, r} + |s|r) where p and q are positive. Furthermore, if r ≤ p − q, then the ribbonlength of T p,q;r,s is less then or equal to 2(p + (|s| − 1)r).