K12a478
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-10 q^2+18 q-25+32 q^{-1} -34 q^{-2} +32 q^{-3} -26 q^{-4} +18 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-25 t^2+46 t-55+46 t^{-1} -25 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+3 z^4+2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-7 a^2 z^4-z^4 a^{-2} +6 z^4-2 a^6 z^2+6 a^4 z^2-6 a^2 z^2-2 z^2 a^{-2} +6 z^2-a^6+2 a^4-2 a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+7 a^4 z^{10}+13 a^2 z^{10}+6 z^{10}+12 a^5 z^9+20 a^3 z^9+15 a z^9+7 z^9 a^{-1} +13 a^6 z^8+9 a^4 z^8-13 a^2 z^8+4 z^8 a^{-2} -5 z^8+9 a^7 z^7-10 a^5 z^7-48 a^3 z^7-48 a z^7-18 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-19 a^6 z^6-40 a^4 z^6-26 a^2 z^6-12 z^6 a^{-2} -21 z^6+a^9 z^5-12 a^7 z^5-6 a^5 z^5+30 a^3 z^5+37 a z^5+11 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+14 a^6 z^4+35 a^4 z^4+34 a^2 z^4+12 z^4 a^{-2} +29 z^4-a^9 z^3+8 a^7 z^3+9 a^5 z^3-8 a^3 z^3-10 a z^3+z^3 a^{-1} +3 z^3 a^{-3} +a^8 z^2-5 a^6 z^2-13 a^4 z^2-14 a^2 z^2-5 z^2 a^{-2} -12 z^2-2 a^7 z-2 a^5 z+a^3 z+a z-z a^{-1} -z a^{-3} +a^6+2 a^4+2 a^2+ a^{-2} +3 }[/math] |
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