K12n519
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-2 q^2+2 q-2+2 q^{-1} - q^{-2} + q^{-3} + q^{-4} - q^{-5} + q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t-3+2 t^{-1} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^2+1 }[/math] |
| Determinant | 7 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-2 a^6+z^4 a^4+4 z^2 a^4+3 a^4+z^2 a^2+a^2-z^4-3 z^2-2+z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^6 z^8+z^8+a^7 z^7+a^5 z^7+2 a z^7+2 z^7 a^{-1} -6 a^6 z^6-a^4 z^6+a^2 z^6+z^6 a^{-2} -3 z^6-6 a^7 z^5-7 a^5 z^5-2 a^3 z^5-10 a z^5-9 z^5 a^{-1} +10 a^6 z^4+3 a^4 z^4-6 a^2 z^4-4 z^4 a^{-2} -3 z^4+10 a^7 z^3+12 a^5 z^3+5 a^3 z^3+12 a z^3+9 z^3 a^{-1} -6 a^6 z^2-5 a^4 z^2+6 a^2 z^2+3 z^2 a^{-2} +8 z^2-4 a^7 z-6 a^5 z-4 a^3 z-4 a z-2 z a^{-1} +2 a^6+3 a^4-a^2- a^{-2} -2 }[/math] |
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