K12a1182
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+7 q^7-14 q^6+21 q^5-27 q^4+30 q^3-28 q^2+24 q-17+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-22 t^2+38 t-45+38 t^{-1} -22 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-8 z^4-z^2+1 }[/math] |
| Determinant | 187 |
| 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^6-5 z^4 a^{-2} -10 z^4 a^{-4} +4 z^4 a^{-6} +3 z^4-z^2 a^{-2} -8 z^2 a^{-4} +5 z^2 a^{-6} +3 z^2+ a^{-2} -2 a^{-4} + a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +12 z^{10} a^{-4} +6 z^{10} a^{-6} +9 z^9 a^{-1} +12 z^9 a^{-3} +10 z^9 a^{-5} +7 z^9 a^{-7} -z^8 a^{-2} -27 z^8 a^{-4} -13 z^8 a^{-6} +5 z^8 a^{-8} +8 z^8+4 a z^7-15 z^7 a^{-1} -37 z^7 a^{-3} -40 z^7 a^{-5} -19 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-20 z^6 a^{-2} +28 z^6 a^{-4} +18 z^6 a^{-6} -11 z^6 a^{-8} +z^6 a^{-10} -17 z^6-8 a z^5+2 z^5 a^{-1} +38 z^5 a^{-3} +63 z^5 a^{-5} +27 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+20 z^4 a^{-2} -15 z^4 a^{-4} -13 z^4 a^{-6} +6 z^4 a^{-8} -3 z^4 a^{-10} +11 z^4+4 a z^3+2 z^3 a^{-1} -16 z^3 a^{-3} -40 z^3 a^{-5} -21 z^3 a^{-7} +5 z^3 a^{-9} +a^2 z^2-5 z^2 a^{-2} +9 z^2 a^{-4} +4 z^2 a^{-6} -z^2 a^{-8} +2 z^2 a^{-10} -6 z^2-a z-z a^{-1} +4 z a^{-3} +8 z a^{-5} +4 z a^{-7} - a^{-2} -2 a^{-4} - a^{-6} +1 }[/math] |
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