K12a439
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-6 q^5+16 q^4-28 q^3+40 q^2-49 q+52-47 q^{-1} +38 q^{-2} -25 q^{-3} +13 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+34 t^2-71 t+91-71 t^{-1} +34 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6+1 }[/math] |
| Determinant | 321 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-4 a^2 z^4-3 z^4 a^{-2} +z^4 a^{-4} +5 z^4+a^4 z^2-3 a^2 z^2-z^2 a^{-2} +3 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a z^{11}+5 z^{11} a^{-1} +14 a^2 z^{10}+17 z^{10} a^{-2} +31 z^{10}+17 a^3 z^9+33 a z^9+39 z^9 a^{-1} +23 z^9 a^{-3} +12 a^4 z^8-4 a^2 z^8-7 z^8 a^{-2} +16 z^8 a^{-4} -39 z^8+5 a^5 z^7-26 a^3 z^7-86 a z^7-100 z^7 a^{-1} -39 z^7 a^{-3} +6 z^7 a^{-5} +a^6 z^6-20 a^4 z^6-30 a^2 z^6-34 z^6 a^{-2} -24 z^6 a^{-4} +z^6 a^{-6} -18 z^6-7 a^5 z^5+13 a^3 z^5+62 a z^5+64 z^5 a^{-1} +17 z^5 a^{-3} -5 z^5 a^{-5} -a^6 z^4+13 a^4 z^4+30 a^2 z^4+24 z^4 a^{-2} +8 z^4 a^{-4} +32 z^4+3 a^5 z^3-2 a^3 z^3-14 a z^3-10 z^3 a^{-1} -z^3 a^{-3} -3 a^4 z^2-9 a^2 z^2-3 z^2 a^{-2} -9 z^2+1 }[/math] |
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