K12a794
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-3 q^{12}+6 q^{11}-9 q^{10}+12 q^9-14 q^8+13 q^7-12 q^6+9 q^5-6 q^4+4 q^3-q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+7 t^3-12 t^2+16 t-17+16 t^{-1} -12 t^{-2} +7 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-9 z^6-10 z^4-z^2+1 }[/math] |
| Determinant | 91 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -6 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} +6 z^4 a^{-4} -13 z^4 a^{-6} -7 z^4 a^{-8} +4 z^4 a^{-10} +11 z^2 a^{-4} -14 z^2 a^{-6} -2 z^2 a^{-8} +4 z^2 a^{-10} +6 a^{-4} -7 a^{-6} + a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +z^{10} a^{-6} +4 z^{10} a^{-8} +3 z^{10} a^{-10} +z^9 a^{-5} -4 z^9 a^{-7} +5 z^9 a^{-11} +z^8 a^{-4} -2 z^8 a^{-6} -17 z^8 a^{-8} -8 z^8 a^{-10} +6 z^8 a^{-12} -4 z^7 a^{-5} +10 z^7 a^{-7} -5 z^7 a^{-9} -13 z^7 a^{-11} +6 z^7 a^{-13} -7 z^6 a^{-4} -8 z^6 a^{-6} +27 z^6 a^{-8} +11 z^6 a^{-10} -12 z^6 a^{-12} +5 z^6 a^{-14} +z^5 a^{-5} -26 z^5 a^{-7} +z^5 a^{-9} +16 z^5 a^{-11} -9 z^5 a^{-13} +3 z^5 a^{-15} +17 z^4 a^{-4} +23 z^4 a^{-6} -25 z^4 a^{-8} -13 z^4 a^{-10} +11 z^4 a^{-12} -6 z^4 a^{-14} +z^4 a^{-16} +9 z^3 a^{-5} +30 z^3 a^{-7} +2 z^3 a^{-9} -10 z^3 a^{-11} +6 z^3 a^{-13} -3 z^3 a^{-15} -17 z^2 a^{-4} -20 z^2 a^{-6} +9 z^2 a^{-8} +6 z^2 a^{-10} -3 z^2 a^{-12} +2 z^2 a^{-14} -z^2 a^{-16} -7 z a^{-5} -11 z a^{-7} -z a^{-9} +2 z a^{-11} -z a^{-13} +6 a^{-4} +7 a^{-6} + a^{-8} - a^{-10} }[/math] |
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