K13n3252

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Polynomial invariants

Jones polynomial Data:K13n3252/Jones Polynomial
Alexander polynomial [math]\displaystyle{ -t^4+5 t^3-11 t^2+16 t-17+16 t^{-1} -11 t^{-2} +5 t^{-3} - t^{-4} }[/math]
Conway polynomial Data:K13n3252/Conway Polynomial
Determinant 83
Signature 2
HOMFLY-PT polynomial [math]\displaystyle{ -z^8+a^2 z^6+z^6 a^{-2} -5 z^6+3 a^2 z^4+3 z^4 a^{-2} -7 z^4+a^2 z^2+z^2 a^{-2} -z^2-a^2- a^{-2} +3 }[/math]
Kauffman polynomial [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +6 a^2 z^{10}+6 z^{10} a^{-2} +12 z^{10}+4 a^3 z^9-7 a z^9-7 z^9 a^{-1} +4 z^9 a^{-3} +a^4 z^8-30 a^2 z^8-30 z^8 a^{-2} +z^8 a^{-4} -62 z^8-19 a^3 z^7-19 a z^7-19 z^7 a^{-1} -19 z^7 a^{-3} -4 a^4 z^6+43 a^2 z^6+43 z^6 a^{-2} -4 z^6 a^{-4} +94 z^6+24 a^3 z^5+46 a z^5+46 z^5 a^{-1} +24 z^5 a^{-3} +3 a^4 z^4-23 a^2 z^4-23 z^4 a^{-2} +3 z^4 a^{-4} -52 z^4-9 a^3 z^3-24 a z^3-24 z^3 a^{-1} -9 z^3 a^{-3} +3 a^2 z^2+3 z^2 a^{-2} +6 z^2+a z+z a^{-1} +a^2+ a^{-2} +3 }[/math]



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