The homfly and the Kauffman bracket polynomials for the generalized mutant of a link

Conwayʹs mutation of a link is achieved by flipping a 2-strand tangle. Two mutant links share the same polynomial invariants. Anstee et al. generalized a mutation by flipping a many-string tangle which has rotational symmetry. We give another generalization of mutation: We consider a link constructed with 3-strand tangles T1, T2,…,Tn and a 2n-strand tangle S. Under some conditions, by permuting T1, T2,…,Tn or flipping S, the homfly or the Kauffman bracket polynomial do not change.