K12n382
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+q^6-q^4+3 q^3-3 q^2+4 q-4+3 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^2+5 t-7+5 t^{-1} - t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^4+z^2+1 }[/math] |
| Determinant | 19 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} +z^4 a^{-4} -z^4+a^2 z^2-2 z^2 a^{-2} +5 z^2 a^{-4} -z^2 a^{-6} -2 z^2+a^2- a^{-2} +4 a^{-4} -2 a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^8 a^{-6} +z^8+2 a z^7+3 z^7 a^{-1} +z^7 a^{-7} +a^2 z^6+3 z^6 a^{-2} -2 z^6 a^{-4} -7 z^6 a^{-6} -z^6-8 a z^5-10 z^5 a^{-1} +z^5 a^{-3} -3 z^5 a^{-5} -6 z^5 a^{-7} -4 a^2 z^4-7 z^4 a^{-2} +9 z^4 a^{-4} +13 z^4 a^{-6} -7 z^4+8 a z^3+8 z^3 a^{-1} +9 z^3 a^{-5} +9 z^3 a^{-7} +4 a^2 z^2+z^2 a^{-2} -10 z^2 a^{-4} -7 z^2 a^{-6} +8 z^2-2 a z-3 z a^{-1} -2 z a^{-3} -4 z a^{-5} -3 z a^{-7} -a^2+ a^{-2} +4 a^{-4} +2 a^{-6} -1 }[/math] |
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