K12n51
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-2 q^2+2 q-1+ q^{-1} + q^{-2} -2 q^{-3} +3 q^{-4} -4 q^{-5} +3 q^{-6} -2 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t+5-2 t^{-1} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-2 z^2 }[/math] |
| Determinant | 9 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-2 z^2 a^6-2 a^6+z^4 a^4+2 z^2 a^4+a^4+a^2-z^4-3 z^2-1+z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^6 z^{10}+a^4 z^{10}+2 a^7 z^9+4 a^5 z^9+2 a^3 z^9+a^8 z^8-3 a^6 z^8-4 a^4 z^8+a^2 z^8+z^8-12 a^7 z^7-25 a^5 z^7-14 a^3 z^7+a z^7+2 z^7 a^{-1} -6 a^8 z^6-7 a^6 z^6-4 a^4 z^6-8 a^2 z^6+z^6 a^{-2} -4 z^6+22 a^7 z^5+46 a^5 z^5+26 a^3 z^5-7 a z^5-9 z^5 a^{-1} +11 a^8 z^4+22 a^6 z^4+18 a^4 z^4+11 a^2 z^4-4 z^4 a^{-2} -16 a^7 z^3-34 a^5 z^3-20 a^3 z^3+6 a z^3+8 z^3 a^{-1} -7 a^8 z^2-14 a^6 z^2-12 a^4 z^2-4 a^2 z^2+3 z^2 a^{-2} +4 z^2+5 a^7 z+10 a^5 z+6 a^3 z-z a^{-1} +a^8+2 a^6+a^4-a^2- a^{-2} -1 }[/math] |
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