K12a713
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+6 q^7-11 q^6+16 q^5-20 q^4+22 q^3-20 q^2+17 q-12+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-17 t^2+27 t-31+27 t^{-1} -17 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-9 z^4-z^2+1 }[/math] |
| Determinant | 139 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +z^6-9 z^4 a^{-2} -8 z^4 a^{-4} +4 z^4 a^{-6} +4 z^4-7 z^2 a^{-2} -3 z^2 a^{-4} +4 z^2 a^{-6} +5 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +5 z^9 a^{-1} +6 z^9 a^{-3} +5 z^9 a^{-5} +4 z^9 a^{-7} -13 z^8 a^{-4} -4 z^8 a^{-6} +4 z^8 a^{-8} +5 z^8+3 a z^7-10 z^7 a^{-1} -18 z^7 a^{-3} -15 z^7 a^{-5} -7 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-13 z^6 a^{-2} +16 z^6 a^{-4} +5 z^6 a^{-6} -9 z^6 a^{-8} +z^6 a^{-10} -13 z^6-8 a z^5+5 z^5 a^{-1} +21 z^5 a^{-3} +20 z^5 a^{-5} +3 z^5 a^{-7} -9 z^5 a^{-9} -3 a^2 z^4+20 z^4 a^{-2} -8 z^4 a^{-4} -7 z^4 a^{-6} +4 z^4 a^{-8} -3 z^4 a^{-10} +11 z^4+5 a z^3-z^3 a^{-1} -8 z^3 a^{-3} -10 z^3 a^{-5} -z^3 a^{-7} +7 z^3 a^{-9} +2 a^2 z^2-12 z^2 a^{-2} +2 z^2 a^{-4} +3 z^2 a^{-6} +2 z^2 a^{-10} -7 z^2-a z-z a^{-1} +z a^{-3} +z a^{-5} -z a^{-7} -z a^{-9} +2 a^{-2} + a^{-4} +2 }[/math] |
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