K12a921
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+7 q^7-14 q^6+20 q^5-25 q^4+28 q^3-26 q^2+22 q-15+9 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-21 t^2+35 t-41+35 t^{-1} -21 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-7 z^4+1 }[/math] |
| Determinant | 175 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +z^6-4 z^4 a^{-2} -10 z^4 a^{-4} +4 z^4 a^{-6} +3 z^4+2 z^2 a^{-2} -9 z^2 a^{-4} +5 z^2 a^{-6} +2 z^2+3 a^{-2} -3 a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +11 z^{10} a^{-4} +5 z^{10} a^{-6} +9 z^9 a^{-1} +9 z^9 a^{-3} +6 z^9 a^{-5} +6 z^9 a^{-7} -7 z^8 a^{-2} -28 z^8 a^{-4} -8 z^8 a^{-6} +5 z^8 a^{-8} +8 z^8+4 a z^7-22 z^7 a^{-1} -33 z^7 a^{-3} -22 z^7 a^{-5} -12 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-6 z^6 a^{-2} +36 z^6 a^{-4} +8 z^6 a^{-6} -11 z^6 a^{-8} +z^6 a^{-10} -21 z^6-9 a z^5+18 z^5 a^{-1} +40 z^5 a^{-3} +29 z^5 a^{-5} +8 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+10 z^4 a^{-2} -25 z^4 a^{-4} -8 z^4 a^{-6} +6 z^4 a^{-8} -3 z^4 a^{-10} +16 z^4+3 a z^3-7 z^3 a^{-1} -17 z^3 a^{-3} -14 z^3 a^{-5} -z^3 a^{-7} +6 z^3 a^{-9} +z^2 a^{-2} +13 z^2 a^{-4} +4 z^2 a^{-6} -z^2 a^{-8} +2 z^2 a^{-10} -5 z^2+z a^{-1} +3 z a^{-3} +z a^{-5} -3 z a^{-7} -2 z a^{-9} -3 a^{-2} -3 a^{-4} - a^{-6} }[/math] |
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