HOMFLY-PT/Kauffman relation via BMW characters proves HZ factorisability for 3-strand knots but fails for 4-strand knots.
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Authors introduce the HZ character expansion of the HOMFLY-PT polynomial, identify hook diagrams for factorisability, and construct an infinite family of HZ-factorisable hyperbolic knots via full, partial-full, and Jucys-Murphy twists, plus a decomposition conjecture proven for three strands.
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