K12a1254
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-12 q^3+17 q^2-21 q+23-21 q^{-1} +17 q^{-2} -12 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+4 t^4-10 t^3+18 t^2-25 t+29-25 t^{-1} +18 t^{-2} -10 t^{-3} +4 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-6 z^8-13 z^6-12 z^4-4 z^2+1 }[/math] |
| Determinant | 145 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -8 z^8+6 a^2 z^6+6 z^6 a^{-2} -25 z^6+13 a^2 z^4+13 z^4 a^{-2} -38 z^4+12 a^2 z^2+12 z^2 a^{-2} -28 z^2+4 a^2+4 a^{-2} -7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+5 z^{10} a^{-2} +10 z^{10}+6 a^3 z^9+2 a z^9+2 z^9 a^{-1} +6 z^9 a^{-3} +5 a^4 z^8-14 a^2 z^8-14 z^8 a^{-2} +5 z^8 a^{-4} -38 z^8+3 a^5 z^7-17 a^3 z^7-19 a z^7-19 z^7 a^{-1} -17 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-13 a^4 z^6+21 a^2 z^6+21 z^6 a^{-2} -13 z^6 a^{-4} +z^6 a^{-6} +70 z^6-8 a^5 z^5+20 a^3 z^5+36 a z^5+36 z^5 a^{-1} +20 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+9 a^4 z^4-20 a^2 z^4-20 z^4 a^{-2} +9 z^4 a^{-4} -3 z^4 a^{-6} -64 z^4+4 a^5 z^3-15 a^3 z^3-22 a z^3-22 z^3 a^{-1} -15 z^3 a^{-3} +4 z^3 a^{-5} +2 a^6 z^2-4 a^4 z^2+12 a^2 z^2+12 z^2 a^{-2} -4 z^2 a^{-4} +2 z^2 a^{-6} +36 z^2+3 a^3 z+5 a z+5 z a^{-1} +3 z a^{-3} -4 a^2-4 a^{-2} -7 }[/math] |
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