K12a876
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{16}-3 q^{15}+6 q^{14}-10 q^{13}+13 q^{12}-16 q^{11}+15 q^{10}-14 q^9+12 q^8-7 q^7+5 q^6-2 q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^4-8 t^3+13 t^2-18 t+21-18 t^{-1} +13 t^{-2} -8 t^{-3} +3 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^8+16 z^6+25 z^4+10 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +2 z^8 a^{-10} +6 z^6 a^{-8} +13 z^6 a^{-10} -3 z^6 a^{-12} +11 z^4 a^{-8} +29 z^4 a^{-10} -16 z^4 a^{-12} +z^4 a^{-14} +6 z^2 a^{-8} +26 z^2 a^{-10} -26 z^2 a^{-12} +4 z^2 a^{-14} + a^{-8} +8 a^{-10} -12 a^{-12} +4 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +3 z^{10} a^{-10} +6 z^{10} a^{-12} +3 z^{10} a^{-14} +2 z^9 a^{-9} +z^9 a^{-11} +4 z^9 a^{-13} +5 z^9 a^{-15} +z^8 a^{-8} -17 z^8 a^{-10} -28 z^8 a^{-12} -3 z^8 a^{-14} +7 z^8 a^{-16} -10 z^7 a^{-9} -21 z^7 a^{-11} -24 z^7 a^{-13} -6 z^7 a^{-15} +7 z^7 a^{-17} -6 z^6 a^{-8} +37 z^6 a^{-10} +56 z^6 a^{-12} -5 z^6 a^{-14} -13 z^6 a^{-16} +5 z^6 a^{-18} +14 z^5 a^{-9} +46 z^5 a^{-11} +39 z^5 a^{-13} -8 z^5 a^{-15} -12 z^5 a^{-17} +3 z^5 a^{-19} +11 z^4 a^{-8} -43 z^4 a^{-10} -69 z^4 a^{-12} +9 z^4 a^{-16} -5 z^4 a^{-18} +z^4 a^{-20} -4 z^3 a^{-9} -42 z^3 a^{-11} -37 z^3 a^{-13} +15 z^3 a^{-15} +11 z^3 a^{-17} -3 z^3 a^{-19} -6 z^2 a^{-8} +28 z^2 a^{-10} +43 z^2 a^{-12} +7 z^2 a^{-14} +z^2 a^{-18} -z^2 a^{-20} +14 z a^{-11} +14 z a^{-13} -4 z a^{-15} -4 z a^{-17} + a^{-8} -8 a^{-10} -12 a^{-12} -4 a^{-14} }[/math] |
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