K12n301
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+3 q^5-6 q^4+9 q^3-10 q^2+11 q-10+8 q^{-1} -5 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-10 t^2+12 t-11+12 t^{-1} -10 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6+z^2+1 }[/math] |
| Determinant | 67 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-13 z^4 a^{-2} +5 z^4 a^{-4} +9 z^4-3 a^2 z^2-13 z^2 a^{-2} +7 z^2 a^{-4} -z^2 a^{-6} +11 z^2-a^2-4 a^{-2} +3 a^{-4} - a^{-6} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+3 a z^9+6 z^9 a^{-1} +3 z^9 a^{-3} +3 a^2 z^8+4 z^8 a^{-2} +3 z^8 a^{-4} +4 z^8+a^3 z^7-10 a z^7-21 z^7 a^{-1} -9 z^7 a^{-3} +z^7 a^{-5} -13 a^2 z^6-26 z^6 a^{-2} -10 z^6 a^{-4} -29 z^6-4 a^3 z^5+5 a z^5+19 z^5 a^{-1} +10 z^5 a^{-3} +16 a^2 z^4+39 z^4 a^{-2} +18 z^4 a^{-4} +3 z^4 a^{-6} +40 z^4+4 a^3 z^3+3 a z^3-5 z^3 a^{-1} -3 z^3 a^{-3} +2 z^3 a^{-5} +z^3 a^{-7} -7 a^2 z^2-23 z^2 a^{-2} -12 z^2 a^{-4} -3 z^2 a^{-6} -21 z^2-a^3 z-2 a z-z a^{-1} -z a^{-5} -z a^{-7} +a^2+4 a^{-2} +3 a^{-4} + a^{-6} +4 }[/math] |
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