HOMFLY-PT/Kauffman relation via BMW characters proves HZ factorisability for 3-strand knots but fails for 4-strand knots.
Murakami, The parallel version of polynomial invariants of links, Osaka J
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A relation between the HOMFLY-PT and Kauffman polynomials via characters
HOMFLY-PT/Kauffman relation via BMW characters proves HZ factorisability for 3-strand knots but fails for 4-strand knots.