The warping degree of a nanoword

A. Kawauchi has introduced the notion of warping degrees of knot diagrams and A. Shimizu has given an inequality for warping degrees and crossing numbers of knot diagrams Shimizu (2010) [4]. In this paper, we extend the notion of warping degrees and Shimizu’s inequality to nanowords. Moreover, to describe the condition for the equality, we introduce the new notion on nanowords, “the alternating nanowords”, which corresponds to the alternating knot diagrams.