K12a839
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-2 q^{12}+4 q^{11}-7 q^{10}+9 q^9-12 q^8+12 q^7-11 q^6+10 q^5-7 q^4+5 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+7 t^3-11 t^2+14 t-15+14 t^{-1} -11 t^{-2} +7 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-9 z^6-9 z^4+z^2+1 }[/math] |
| Determinant | 83 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -6 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -6 z^4 a^{-6} -13 z^4 a^{-8} +5 z^4 a^{-10} +7 z^2 a^{-4} +z^2 a^{-6} -14 z^2 a^{-8} +7 z^2 a^{-10} +2 a^{-4} +3 a^{-6} -7 a^{-8} +3 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +5 z^{10} a^{-8} +3 z^{10} a^{-10} +2 z^9 a^{-5} -z^9 a^{-7} +z^9 a^{-9} +4 z^9 a^{-11} +z^8 a^{-4} -8 z^8 a^{-6} -24 z^8 a^{-8} -11 z^8 a^{-10} +4 z^8 a^{-12} -10 z^7 a^{-5} -9 z^7 a^{-7} -16 z^7 a^{-9} -13 z^7 a^{-11} +4 z^7 a^{-13} -6 z^6 a^{-4} +7 z^6 a^{-6} +45 z^6 a^{-8} +19 z^6 a^{-10} -10 z^6 a^{-12} +3 z^6 a^{-14} +14 z^5 a^{-5} +16 z^5 a^{-7} +31 z^5 a^{-9} +17 z^5 a^{-11} -10 z^5 a^{-13} +2 z^5 a^{-15} +12 z^4 a^{-4} -2 z^4 a^{-6} -52 z^4 a^{-8} -22 z^4 a^{-10} +10 z^4 a^{-12} -5 z^4 a^{-14} +z^4 a^{-16} -4 z^3 a^{-5} -12 z^3 a^{-7} -31 z^3 a^{-9} -7 z^3 a^{-11} +13 z^3 a^{-13} -3 z^3 a^{-15} -9 z^2 a^{-4} +6 z^2 a^{-6} +31 z^2 a^{-8} +11 z^2 a^{-10} +3 z^2 a^{-14} -2 z^2 a^{-16} -z a^{-5} +6 z a^{-7} +10 z a^{-9} -z a^{-11} -4 z a^{-13} +2 a^{-4} -3 a^{-6} -7 a^{-8} -3 a^{-10} }[/math] |
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