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The homfly and the Kauffman bracket polynomials for the generalized mutant of a link. (English) Zbl 0827.57006

Summary: Conway’s mutation of a link is achieved by flipping a 2-strand tangle. Two mutant links share the same polynomial invariants. R. Anstee, J. Przytycki and D. Rolfsen [Topology Appl. 32, 237-249 (1989; Zbl 0638.57006)] generalized a mutation of flipping a many-string tangle which has rotational symmetry. We give another generalization of mutation: We consider a link constructed with 3-strand tangles \(T_1, T_2, \dots, T_n\) and a \(2n\)-strand tangle \(S\). Under some conditions, by permuting \(T_1, T_2, \dots, T_n\) or flipping \(S\), the homfly or the Kauffman bracket polynomial do not change.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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