K12n31
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+4 q^4-4 q^3+4 q^2-2 q+1+ q^{-1} -3 q^{-2} +3 q^{-3} -2 q^{-4} + q^{-5} }[/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{ -z^6 a^{-2} +z^6-2 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +6 z^4+a^4 z^2-7 a^2 z^2-8 z^2 a^{-2} +2 z^2 a^{-4} +10 z^2+2 a^4-5 a^2-3 a^{-2} + a^{-4} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+2 a^3 z^9+4 a z^9+3 z^9 a^{-1} +z^9 a^{-3} +a^4 z^8-3 a^2 z^8+4 z^8 a^{-2} +3 z^8 a^{-4} -3 z^8-12 a^3 z^7-27 a z^7-20 z^7 a^{-1} -2 z^7 a^{-3} +3 z^7 a^{-5} -6 a^4 z^6-10 a^2 z^6-25 z^6 a^{-2} -12 z^6 a^{-4} +z^6 a^{-6} -16 z^6+21 a^3 z^5+49 a z^5+32 z^5 a^{-1} -7 z^5 a^{-3} -11 z^5 a^{-5} +11 a^4 z^4+31 a^2 z^4+40 z^4 a^{-2} +10 z^4 a^{-4} -3 z^4 a^{-6} +47 z^4-15 a^3 z^3-31 a z^3-15 z^3 a^{-1} +8 z^3 a^{-3} +7 z^3 a^{-5} -8 a^4 z^2-24 a^2 z^2-22 z^2 a^{-2} -5 z^2 a^{-4} +z^2 a^{-6} -32 z^2+4 a^3 z+7 a z+3 z a^{-1} -z a^{-3} -z a^{-5} +2 a^4+5 a^2+3 a^{-2} + a^{-4} +6 }[/math] |
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