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