K12a587
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-4 q^{12}+9 q^{11}-16 q^{10}+22 q^9-26 q^8+27 q^7-25 q^6+20 q^5-13 q^4+8 q^3-3 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-22 t^2+34 t-39+34 t^{-1} -22 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-2 z^4+4 z^2+1 }[/math] |
| Determinant | 175 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -4 z^6 a^{-6} -4 z^6 a^{-8} +z^6 a^{-10} +4 z^4 a^{-4} -4 z^4 a^{-6} -5 z^4 a^{-8} +3 z^4 a^{-10} +5 z^2 a^{-4} -3 z^2 a^{-8} +2 z^2 a^{-10} +2 a^{-4} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +4 z^{10} a^{-6} +12 z^{10} a^{-8} +8 z^{10} a^{-10} +3 z^9 a^{-5} +4 z^9 a^{-7} +16 z^9 a^{-9} +15 z^9 a^{-11} +z^8 a^{-4} -13 z^8 a^{-6} -34 z^8 a^{-8} -2 z^8 a^{-10} +18 z^8 a^{-12} -13 z^7 a^{-5} -36 z^7 a^{-7} -63 z^7 a^{-9} -25 z^7 a^{-11} +15 z^7 a^{-13} -5 z^6 a^{-4} +7 z^6 a^{-6} +16 z^6 a^{-8} -37 z^6 a^{-10} -32 z^6 a^{-12} +9 z^6 a^{-14} +18 z^5 a^{-5} +50 z^5 a^{-7} +57 z^5 a^{-9} +z^5 a^{-11} -20 z^5 a^{-13} +4 z^5 a^{-15} +9 z^4 a^{-4} +9 z^4 a^{-6} +11 z^4 a^{-8} +35 z^4 a^{-10} +17 z^4 a^{-12} -6 z^4 a^{-14} +z^4 a^{-16} -8 z^3 a^{-5} -22 z^3 a^{-7} -16 z^3 a^{-9} +8 z^3 a^{-11} +9 z^3 a^{-13} -z^3 a^{-15} -7 z^2 a^{-4} -6 z^2 a^{-6} -4 z^2 a^{-8} -9 z^2 a^{-10} -3 z^2 a^{-12} +z^2 a^{-14} +3 z a^{-7} +z a^{-9} -3 z a^{-11} -z a^{-13} +2 a^{-4} - a^{-8} }[/math] |
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