K12a926
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+6 q^7-11 q^6+15 q^5-18 q^4+20 q^3-18 q^2+15 q-10+6 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-16 t^2+24 t-27+24 t^{-1} -16 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-8 z^4+1 }[/math] |
| Determinant | 127 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +z^6-8 z^4 a^{-2} -8 z^4 a^{-4} +4 z^4 a^{-6} +4 z^4-4 z^2 a^{-2} -4 z^2 a^{-4} +4 z^2 a^{-6} +4 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +9 z^{10} a^{-4} +4 z^{10} a^{-6} +6 z^9 a^{-1} -2 z^9 a^{-5} +4 z^9 a^{-7} -17 z^8 a^{-2} -38 z^8 a^{-4} -12 z^8 a^{-6} +4 z^8 a^{-8} +5 z^8+3 a z^7-21 z^7 a^{-1} -20 z^7 a^{-3} -6 z^7 a^{-5} -7 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6+20 z^6 a^{-2} +67 z^6 a^{-4} +20 z^6 a^{-6} -9 z^6 a^{-8} +z^6 a^{-10} -16 z^6-9 a z^5+25 z^5 a^{-1} +45 z^5 a^{-3} +18 z^5 a^{-5} -2 z^5 a^{-7} -9 z^5 a^{-9} -3 a^2 z^4-4 z^4 a^{-2} -45 z^4 a^{-4} -20 z^4 a^{-6} +2 z^4 a^{-8} -3 z^4 a^{-10} +13 z^4+4 a z^3-13 z^3 a^{-1} -26 z^3 a^{-3} -10 z^3 a^{-5} +6 z^3 a^{-7} +7 z^3 a^{-9} +a^2 z^2-2 z^2 a^{-2} +12 z^2 a^{-4} +7 z^2 a^{-6} +z^2 a^{-8} +2 z^2 a^{-10} -5 z^2+2 z a^{-1} +4 z a^{-3} -4 z a^{-7} -2 z a^{-9} +1 }[/math] |
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