K12a888
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-13 q^6+24 q^5-36 q^4+45 q^3-48 q^2+46 q-37+26 q^{-1} -15 q^{-2} +6 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-33 t^2+67 t-83+67 t^{-1} -33 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+z^4+1 }[/math] |
| Determinant | 303 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-4 z^4 a^{-2} +4 z^4 a^{-4} -z^4 a^{-6} +3 z^4+2 z^2 a^{-4} -z^2 a^{-6} -z^2+a^2+3 a^{-2} - a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 6 z^{11} a^{-1} +6 z^{11} a^{-3} +33 z^{10} a^{-2} +18 z^{10} a^{-4} +15 z^{10}+14 a z^9+21 z^9 a^{-1} +32 z^9 a^{-3} +25 z^9 a^{-5} +6 a^2 z^8-67 z^8 a^{-2} -10 z^8 a^{-4} +22 z^8 a^{-6} -29 z^8+a^3 z^7-35 a z^7-86 z^7 a^{-1} -99 z^7 a^{-3} -36 z^7 a^{-5} +13 z^7 a^{-7} -12 a^2 z^6+21 z^6 a^{-2} -30 z^6 a^{-4} -30 z^6 a^{-6} +5 z^6 a^{-8} +4 z^6-a^3 z^5+23 a z^5+69 z^5 a^{-1} +74 z^5 a^{-3} +16 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +5 a^2 z^4+10 z^4 a^{-2} +25 z^4 a^{-4} +16 z^4 a^{-6} -2 z^4 a^{-8} +8 z^4-a z^3-11 z^3 a^{-1} -18 z^3 a^{-3} -4 z^3 a^{-5} +4 z^3 a^{-7} +a^2 z^2+z^2 a^{-2} -4 z^2 a^{-4} -3 z^2 a^{-6} +3 z^2-a z-z a^{-1} +z a^{-3} +z a^{-5} -a^2-3 a^{-2} - a^{-4} -2 }[/math] |
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