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We give an explicit formula for the HOMFLY polynomial of a rational link (in particular, knot) in terms of a special continued fraction for the rational number that defines the given link [after this work was accomplished, the authors learned about a paper by Nakabo (J. Knot Theory Ramif 11(4):565–574, 2002) where a similar result was proved. However, Nakabo’s formula is different from ours, and his proof is longer and less clear].
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Duzhin et al. (2015) studied this question.
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