K12n570
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ - q^{-1} +3 q^{-2} -3 q^{-3} +6 q^{-4} -7 q^{-5} +7 q^{-6} -7 q^{-7} +5 q^{-8} -3 q^{-9} +2 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-3 t^3+6 t^2-8 t+9-8 t^{-1} +6 t^{-2} -3 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+5 z^6+8 z^4+5 z^2+1 }[/math] |
| Determinant | 45 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-5 z^4 a^8-7 z^2 a^8-2 a^8+z^8 a^6+7 z^6 a^6+17 z^4 a^6+15 z^2 a^6+2 a^6-z^6 a^4-4 z^4 a^4-3 z^2 a^4+a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-3 z^3 a^{13}+z a^{13}+2 z^6 a^{12}-6 z^4 a^{12}+3 z^2 a^{12}+2 z^7 a^{11}-5 z^5 a^{11}+2 z^3 a^{11}+2 z^8 a^{10}-6 z^6 a^{10}+6 z^4 a^{10}-z^2 a^{10}+2 z^9 a^9-9 z^7 a^9+17 z^5 a^9-10 z^3 a^9+2 z a^9+z^{10} a^8-4 z^8 a^8+7 z^6 a^8-4 z^4 a^8+6 z^2 a^8-2 a^8+3 z^9 a^7-16 z^7 a^7+34 z^5 a^7-25 z^3 a^7+4 z a^7+z^{10} a^6-6 z^8 a^6+18 z^6 a^6-26 z^4 a^6+16 z^2 a^6-2 a^6+z^9 a^5-5 z^7 a^5+12 z^5 a^5-13 z^3 a^5+2 z a^5+3 z^6 a^4-10 z^4 a^4+6 z^2 a^4+a^4+z^5 a^3-3 z^3 a^3+z a^3 }[/math] |
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