K12a511
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-6 q^{-1} +11 q^{-2} -14 q^{-3} +18 q^{-4} -19 q^{-5} +18 q^{-6} -15 q^{-7} +10 q^{-8} -6 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+17 t^2-23 t+25-23 t^{-1} +17 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+9 z^4+5 z^2+1 }[/math] |
| Determinant | 125 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-4 z^2 a^8-a^8+z^8 a^6+5 z^6 a^6+8 z^4 a^6+4 z^2 a^6-a^6+z^8 a^4+5 z^6 a^4+9 z^4 a^4+9 z^2 a^4+4 a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-6 z^4 a^{12}+3 z^2 a^{12}+4 z^7 a^{11}-5 z^5 a^{11}+z a^{11}+4 z^8 a^{10}-2 z^6 a^{10}-4 z^4 a^{10}+2 z^2 a^{10}+4 z^9 a^9-5 z^7 a^9+7 z^5 a^9-8 z^3 a^9+3 z a^9+3 z^{10} a^8-4 z^8 a^8+7 z^6 a^8-9 z^4 a^8+6 z^2 a^8-a^8+z^{11} a^7+5 z^9 a^7-19 z^7 a^7+26 z^5 a^7-14 z^3 a^7+2 z a^7+6 z^{10} a^6-16 z^8 a^6+14 z^6 a^6-5 z^4 a^6+z^2 a^6+a^6+z^{11} a^5+5 z^9 a^5-24 z^7 a^5+25 z^5 a^5-6 z^3 a^5-2 z a^5+3 z^{10} a^4-5 z^8 a^4-10 z^6 a^4+20 z^4 a^4-13 z^2 a^4+4 a^4+4 z^9 a^3-13 z^7 a^3+8 z^5 a^3+2 z^3 a^3-2 z a^3+3 z^8 a^2-12 z^6 a^2+14 z^4 a^2-7 z^2 a^2+a^2+z^7 a-4 z^5 a+4 z^3 a-z a }[/math] |
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