K12a47
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-17 q^9+24 q^8-29 q^7+31 q^6-28 q^5+23 q^4-15 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+19 t^2-45 t+59-45 t^{-1} +19 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+z^4+4 z^2+1 }[/math] |
| Determinant | 193 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} +z^4 a^{-2} -z^4 a^{-4} -4 z^4 a^{-6} +5 z^4 a^{-8} +2 z^2 a^{-2} -3 z^2 a^{-6} +9 z^2 a^{-8} -4 z^2 a^{-10} + a^{-2} - a^{-6} +4 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +4 z^{10} a^{-6} +8 z^{10} a^{-8} +4 z^{10} a^{-10} +6 z^9 a^{-5} +15 z^9 a^{-7} +16 z^9 a^{-9} +7 z^9 a^{-11} +5 z^8 a^{-4} +5 z^8 a^{-6} +4 z^8 a^{-8} +11 z^8 a^{-10} +7 z^8 a^{-12} +3 z^7 a^{-3} -7 z^7 a^{-5} -31 z^7 a^{-7} -29 z^7 a^{-9} -4 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -8 z^6 a^{-4} -21 z^6 a^{-6} -37 z^6 a^{-8} -39 z^6 a^{-10} -13 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +22 z^5 a^{-7} +8 z^5 a^{-9} -16 z^5 a^{-11} -9 z^5 a^{-13} -3 z^4 a^{-2} +2 z^4 a^{-4} +20 z^4 a^{-6} +42 z^4 a^{-8} +36 z^4 a^{-10} +7 z^4 a^{-12} -2 z^4 a^{-14} +5 z^3 a^{-3} +3 z^3 a^{-5} -6 z^3 a^{-7} +8 z^3 a^{-9} +19 z^3 a^{-11} +7 z^3 a^{-13} +3 z^2 a^{-2} +z^2 a^{-4} -8 z^2 a^{-6} -20 z^2 a^{-8} -17 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} -z a^{-3} -2 z a^{-5} -4 z a^{-9} -7 z a^{-11} -2 z a^{-13} - a^{-2} + a^{-6} +4 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
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