K12a577
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-6 q^{-1} +11 q^{-2} -14 q^{-3} +17 q^{-4} -18 q^{-5} +17 q^{-6} -13 q^{-7} +9 q^{-8} -5 q^{-9} +2 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+15 t^2-22 t+25-22 t^{-1} +15 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+13 z^4+7 z^2+1 }[/math] |
| Determinant | 117 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-5 z^4 a^8-8 z^2 a^8-4 a^8+z^8 a^6+6 z^6 a^6+14 z^4 a^6+15 z^2 a^6+6 a^6+z^8 a^4+5 z^6 a^4+8 z^4 a^4+4 z^2 a^4-a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-3 z^3 a^{13}+2 z a^{13}+2 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+3 z^7 a^{11}-5 z^5 a^{11}+2 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-9 z^6 a^{10}+12 z^4 a^{10}-7 z^2 a^{10}+4 z^9 a^9-9 z^7 a^9+11 z^5 a^9-2 z^3 a^9+3 z^{10} a^8-6 z^8 a^8+8 z^6 a^8-7 z^4 a^8+11 z^2 a^8-4 a^8+z^{11} a^7+4 z^9 a^7-18 z^7 a^7+27 z^5 a^7-17 z^3 a^7+6 z a^7+6 z^{10} a^6-20 z^8 a^6+33 z^6 a^6-39 z^4 a^6+25 z^2 a^6-6 a^6+z^{11} a^5+4 z^9 a^5-21 z^7 a^5+28 z^5 a^5-21 z^3 a^5+5 z a^5+3 z^{10} a^4-7 z^8 a^4+2 z^6 a^4-2 z^4 a^4+z^2 a^4-a^4+4 z^9 a^3-14 z^7 a^3+14 z^5 a^3-7 z^3 a^3+2 z a^3+3 z^8 a^2-12 z^6 a^2+14 z^4 a^2-5 z^2 a^2+z^7 a-4 z^5 a+4 z^3 a }[/math] |
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