On the classification of a large set of rational 3-tangle diagrams

Abstract

We note that a rational 3-tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational 3-tangle diagrams up to isotopy: [B. Kwon, An algorithm to classify rational 3-tangles, J. Knot Theory Ramifications 24(1) (2015) 1550004]. However, there is no perfect classification about rational 3-tangle diagrams such as the classification of rational 2-tangle diagrams corresponding to rational numbers. In this paper, we classify a large set of rational 3-tangles which are generated by only three generators.