K12n776
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+5 q^5-10 q^4+14 q^3-17 q^2+18 q-16+13 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-15 t^2+21 t-21+21 t^{-1} -15 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+z^4-z^2+1 }[/math] |
| Determinant | 107 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-9 z^4 a^{-2} +4 z^4 a^{-4} +7 z^4-2 a^2 z^2-8 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +6 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-2} +3 z^{10}+6 a z^9+14 z^9 a^{-1} +8 z^9 a^{-3} +4 a^2 z^8+4 z^8 a^{-2} +7 z^8 a^{-4} +z^8+a^3 z^7-20 a z^7-47 z^7 a^{-1} -24 z^7 a^{-3} +2 z^7 a^{-5} -14 a^2 z^6-35 z^6 a^{-2} -18 z^6 a^{-4} -31 z^6-3 a^3 z^5+17 a z^5+46 z^5 a^{-1} +29 z^5 a^{-3} +3 z^5 a^{-5} +14 a^2 z^4+42 z^4 a^{-2} +23 z^4 a^{-4} +5 z^4 a^{-6} +38 z^4+2 a^3 z^3-5 a z^3-19 z^3 a^{-1} -15 z^3 a^{-3} -2 z^3 a^{-5} +z^3 a^{-7} -5 a^2 z^2-18 z^2 a^{-2} -10 z^2 a^{-4} -2 z^2 a^{-6} -15 z^2+a z+3 z a^{-1} +2 z a^{-3} +2 a^{-2} + a^{-4} +2 }[/math] |
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