K12a911
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-17 q^6+24 q^5-29 q^4+30 q^3-28 q^2+22 q-14+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-23 t^2+39 t-45+39 t^{-1} -23 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-9 z^4-4 z^2+1 }[/math] |
| Determinant | 191 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-11 z^4 a^{-2} -5 z^4 a^{-4} +3 z^4 a^{-6} +4 z^4-12 z^2 a^{-2} -z^2 a^{-4} +3 z^2 a^{-6} +6 z^2-5 a^{-2} + a^{-4} + a^{-6} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +11 z^{10} a^{-4} +6 z^{10} a^{-6} +7 z^9 a^{-1} +8 z^9 a^{-3} +10 z^9 a^{-5} +9 z^9 a^{-7} -2 z^8 a^{-2} -19 z^8 a^{-4} -3 z^8 a^{-6} +8 z^8 a^{-8} +6 z^8+3 a z^7-15 z^7 a^{-1} -19 z^7 a^{-3} -21 z^7 a^{-5} -16 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-15 z^6 a^{-2} +15 z^6 a^{-4} -5 z^6 a^{-6} -17 z^6 a^{-8} +z^6 a^{-10} -16 z^6-7 a z^5+13 z^5 a^{-1} +10 z^5 a^{-3} +7 z^5 a^{-5} +9 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+31 z^4 a^{-2} -8 z^4 a^{-4} -5 z^4 a^{-6} +11 z^4 a^{-8} -2 z^4 a^{-10} +18 z^4+3 a z^3-4 z^3 a^{-1} +8 z^3 a^{-3} +5 z^3 a^{-5} -6 z^3 a^{-7} +4 z^3 a^{-9} +2 a^2 z^2-22 z^2 a^{-2} +3 z^2 a^{-4} +6 z^2 a^{-6} -3 z^2 a^{-8} +z^2 a^{-10} -13 z^2-z a^{-1} -5 z a^{-3} -3 z a^{-5} +z a^{-7} +5 a^{-2} + a^{-4} - a^{-6} +4 }[/math] |
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