K12n742
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+4 q^{-1} -7 q^{-2} +12 q^{-3} -14 q^{-4} +15 q^{-5} -14 q^{-6} +11 q^{-7} -8 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-9 t^2+21 t-27+21 t^{-1} -9 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+3 z^4+3 z^2+1 }[/math] |
| Determinant | 91 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8+z^6 a^6+2 z^4 a^6-2 a^6+z^6 a^4+3 z^4 a^4+5 z^2 a^4+3 a^4-z^4 a^2-z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-14 z^6 a^{10}+13 z^4 a^{10}-3 z^2 a^{10}+5 z^9 a^9-15 z^7 a^9+6 z^5 a^9+6 z^3 a^9-2 z a^9+2 z^{10} a^8+3 z^8 a^8-27 z^6 a^8+25 z^4 a^8-4 z^2 a^8+9 z^9 a^7-25 z^7 a^7+11 z^5 a^7+6 z^3 a^7-4 z a^7+2 z^{10} a^6+2 z^8 a^6-17 z^6 a^6+15 z^4 a^6-6 z^2 a^6+2 a^6+4 z^9 a^5-8 z^7 a^5+5 z^5 a^5+z^3 a^5-3 z a^5+3 z^8 a^4-4 z^6 a^4+7 z^4 a^4-7 z^2 a^4+3 a^4+z^7 a^3+3 z^5 a^3-z^3 a^3+4 z^4 a^2-2 z^2 a^2+z^3 a }[/math] |
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