K12a1159
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+7 q^8-11 q^7+14 q^6-17 q^5+17 q^4-15 q^3+12 q^2-8 q+5-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+14 t^2-24 t+29-24 t^{-1} +14 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-10 z^4-4 z^2+1 }[/math] |
| Determinant | 113 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -2 z^6 a^{-4} -z^6 a^{-6} -3 z^4 a^{-2} -7 z^4 a^{-4} -2 z^4 a^{-6} +z^4 a^{-8} +z^4-2 z^2 a^{-2} -7 z^2 a^{-4} +2 z^2 a^{-8} +3 z^2-2 a^{-4} + a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10} a^{-6} +2 z^9 a^{-1} +4 z^9 a^{-5} +6 z^9 a^{-7} -7 z^8 a^{-2} -16 z^8 a^{-4} +8 z^8 a^{-8} +z^8-10 z^7 a^{-1} -9 z^7 a^{-3} -17 z^7 a^{-5} -10 z^7 a^{-7} +8 z^7 a^{-9} +3 z^6 a^{-2} +15 z^6 a^{-4} -14 z^6 a^{-6} -14 z^6 a^{-8} +6 z^6 a^{-10} -6 z^6+15 z^5 a^{-1} +7 z^5 a^{-3} +14 z^5 a^{-5} +7 z^5 a^{-7} -12 z^5 a^{-9} +3 z^5 a^{-11} +7 z^4 a^{-2} -12 z^4 a^{-4} +13 z^4 a^{-6} +12 z^4 a^{-8} -7 z^4 a^{-10} +z^4 a^{-12} +12 z^4-6 z^3 a^{-1} +4 z^3 a^{-3} -8 z^3 a^{-5} -7 z^3 a^{-7} +9 z^3 a^{-9} -2 z^3 a^{-11} -4 z^2 a^{-2} +10 z^2 a^{-4} -6 z^2 a^{-6} -6 z^2 a^{-8} +4 z^2 a^{-10} -z^2 a^{-12} -9 z^2-z a^{-1} -z a^{-3} +3 z a^{-5} +z a^{-7} -2 z a^{-9} -2 a^{-4} + a^{-8} +2 }[/math] |
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