K12n37
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+3 q^6-5 q^5+6 q^4-6 q^3+6 q^2-5 q+4-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+8 t^2-5 t+3-5 t^{-1} +8 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6-2 z^4-2 z^2+1 }[/math] |
| Determinant | 41 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -10 z^4 a^{-2} +12 z^4 a^{-4} -5 z^4 a^{-6} +z^4-13 z^2 a^{-2} +12 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} +4 z^2-5 a^{-2} +5 a^{-4} -3 a^{-6} + a^{-8} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +2 z^9 a^{-1} +5 z^9 a^{-3} +3 z^9 a^{-5} -z^8 a^{-2} +z^8 a^{-4} +3 z^8 a^{-6} +z^8-11 z^7 a^{-1} -25 z^7 a^{-3} -13 z^7 a^{-5} +z^7 a^{-7} -16 z^6 a^{-2} -23 z^6 a^{-4} -13 z^6 a^{-6} -6 z^6+18 z^5 a^{-1} +34 z^5 a^{-3} +15 z^5 a^{-5} -z^5 a^{-7} +37 z^4 a^{-2} +40 z^4 a^{-4} +18 z^4 a^{-6} +3 z^4 a^{-8} +12 z^4-10 z^3 a^{-1} -14 z^3 a^{-3} -8 z^3 a^{-5} -2 z^3 a^{-7} +2 z^3 a^{-9} -25 z^2 a^{-2} -23 z^2 a^{-4} -13 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} -10 z^2+z a^{-1} +2 z a^{-3} +2 z a^{-5} -z a^{-9} +5 a^{-2} +5 a^{-4} +3 a^{-6} + a^{-8} +3 }[/math] |
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