K12a524
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+7 q^7-13 q^6+19 q^5-25 q^4+27 q^3-25 q^2+22 q-15+9 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-15 t^2+41 t-55+41 t^{-1} -15 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-3 z^4-z^2+1 }[/math] |
| Determinant | 171 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2-z^2 a^{-2} +2 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} -z^2+ a^{-4} -2 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +4 z^{10} a^{-2} +7 z^{10} a^{-4} +3 z^{10} a^{-6} +7 z^9 a^{-1} +12 z^9 a^{-3} +10 z^9 a^{-5} +5 z^9 a^{-7} +4 z^8 a^{-2} -3 z^8 a^{-4} +5 z^8 a^{-6} +5 z^8 a^{-8} +7 z^8+4 a z^7-10 z^7 a^{-1} -27 z^7 a^{-3} -23 z^7 a^{-5} -7 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-22 z^6 a^{-2} -17 z^6 a^{-4} -24 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} -15 z^6-9 a z^5+22 z^5 a^{-3} +21 z^5 a^{-5} -8 z^5 a^{-9} -2 a^2 z^4+21 z^4 a^{-2} +27 z^4 a^{-4} +30 z^4 a^{-6} +10 z^4 a^{-8} -3 z^4 a^{-10} +9 z^4+5 a z^3-11 z^3 a^{-3} -9 z^3 a^{-5} +3 z^3 a^{-7} +6 z^3 a^{-9} +a^2 z^2-10 z^2 a^{-2} -13 z^2 a^{-4} -14 z^2 a^{-6} -5 z^2 a^{-8} +2 z^2 a^{-10} -3 z^2+z a^{-1} +4 z a^{-3} +4 z a^{-5} -z a^{-7} -2 z a^{-9} + a^{-4} +2 a^{-6} + a^{-8} +1 }[/math] |
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