K12a508
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+6 q^{10}-11 q^9+16 q^8-19 q^7+20 q^6-19 q^5+15 q^4-10 q^3+6 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-28 t+33-28 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-8 z^4+1 }[/math] |
| Determinant | 129 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -2 z^4 a^{-4} -6 z^4 a^{-6} -2 z^4 a^{-8} +z^4 a^{-10} +3 z^2 a^{-2} -5 z^2 a^{-6} +2 z^2 a^{-10} +2 a^{-2} -2 a^{-6} + a^{-8} }[/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} +3 z^9 a^{-5} +2 z^9 a^{-7} +3 z^9 a^{-9} +4 z^9 a^{-11} +3 z^8 a^{-4} +z^8 a^{-6} -11 z^8 a^{-8} -5 z^8 a^{-10} +4 z^8 a^{-12} +2 z^7 a^{-3} -4 z^7 a^{-5} -2 z^7 a^{-7} -6 z^7 a^{-9} -7 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -6 z^6 a^{-4} -8 z^6 a^{-6} +17 z^6 a^{-8} +8 z^6 a^{-10} -9 z^6 a^{-12} +z^6 a^{-14} -5 z^5 a^{-3} +z^5 a^{-5} +5 z^5 a^{-9} +2 z^5 a^{-11} -9 z^5 a^{-13} -4 z^4 a^{-2} +2 z^4 a^{-4} +12 z^4 a^{-6} -10 z^4 a^{-8} -9 z^4 a^{-10} +4 z^4 a^{-12} -3 z^4 a^{-14} +2 z^3 a^{-3} -2 z^3 a^{-5} +z^3 a^{-7} -z^3 a^{-9} +z^3 a^{-11} +7 z^3 a^{-13} +5 z^2 a^{-2} -9 z^2 a^{-6} +2 z^2 a^{-10} +2 z^2 a^{-14} +z a^{-3} +z a^{-5} -z a^{-11} -z a^{-13} -2 a^{-2} +2 a^{-6} + a^{-8} }[/math] |
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