K12a175
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-3 q^2+8 q-14+21 q^{-1} -27 q^{-2} +29 q^{-3} -27 q^{-4} +23 q^{-5} -16 q^{-6} +9 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-16 t^2+44 t-59+44 t^{-1} -16 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-4 z^4-2 z^2+1 }[/math] |
| Determinant | 183 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-2 z^4 a^6-z^2 a^6+z^6 a^4+a^4+z^6 a^2-z^2 a^2-a^2-2 z^4-2 z^2+z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+4 a^6 z^{10}+7 a^4 z^{10}+3 a^2 z^{10}+7 a^7 z^9+13 a^5 z^9+11 a^3 z^9+5 a z^9+7 a^8 z^8+7 a^6 z^8+3 a^4 z^8+8 a^2 z^8+5 z^8+4 a^9 z^7-7 a^7 z^7-21 a^5 z^7-16 a^3 z^7-3 a z^7+3 z^7 a^{-1} +a^{10} z^6-14 a^8 z^6-27 a^6 z^6-27 a^4 z^6-25 a^2 z^6+z^6 a^{-2} -9 z^6-9 a^9 z^5-8 a^7 z^5-a^3 z^5-7 a z^5-7 z^5 a^{-1} -2 a^{10} z^4+8 a^8 z^4+21 a^6 z^4+26 a^4 z^4+22 a^2 z^4-3 z^4 a^{-2} +4 z^4+6 a^9 z^3+10 a^7 z^3+12 a^5 z^3+9 a^3 z^3+6 a z^3+5 z^3 a^{-1} +a^{10} z^2-2 a^8 z^2-6 a^6 z^2-9 a^4 z^2-9 a^2 z^2+3 z^2 a^{-2} -a^9 z-3 a^7 z-4 a^5 z-2 a^3 z-a z-z a^{-1} +a^4+a^2- a^{-2} }[/math] |
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