K12a723
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-2 q^{12}+3 q^{11}-6 q^{10}+7 q^9-8 q^8+9 q^7-8 q^6+7 q^5-5 q^4+4 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+7 t^3-9 t^2+9 t-9+9 t^{-1} -9 t^{-2} +7 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-9 z^6-7 z^4+4 z^2+1 }[/math] |
| Determinant | 63 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -6 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -5 z^4 a^{-6} -12 z^4 a^{-8} +5 z^4 a^{-10} +6 z^2 a^{-4} +3 z^2 a^{-6} -11 z^2 a^{-8} +6 z^2 a^{-10} + a^{-4} +3 a^{-6} -4 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +4 z^{10} a^{-8} +2 z^{10} a^{-10} +2 z^9 a^{-5} -3 z^9 a^{-7} -3 z^9 a^{-9} +2 z^9 a^{-11} +z^8 a^{-4} -10 z^8 a^{-6} -22 z^8 a^{-8} -9 z^8 a^{-10} +2 z^8 a^{-12} -11 z^7 a^{-5} -2 z^7 a^{-7} +z^7 a^{-9} -6 z^7 a^{-11} +2 z^7 a^{-13} -6 z^6 a^{-4} +14 z^6 a^{-6} +44 z^6 a^{-8} +18 z^6 a^{-10} -4 z^6 a^{-12} +2 z^6 a^{-14} +17 z^5 a^{-5} +8 z^5 a^{-7} +3 z^5 a^{-9} +8 z^5 a^{-11} -2 z^5 a^{-13} +2 z^5 a^{-15} +11 z^4 a^{-4} -9 z^4 a^{-6} -46 z^4 a^{-8} -18 z^4 a^{-10} +5 z^4 a^{-12} -2 z^4 a^{-14} +z^4 a^{-16} -7 z^3 a^{-5} -6 z^3 a^{-7} -6 z^3 a^{-9} -3 z^3 a^{-11} -4 z^3 a^{-15} -7 z^2 a^{-4} +8 z^2 a^{-6} +23 z^2 a^{-8} +5 z^2 a^{-10} -z^2 a^{-12} -2 z^2 a^{-16} +3 z a^{-7} +z a^{-9} -z a^{-11} +3 z a^{-13} +2 z a^{-15} + a^{-4} -3 a^{-6} -4 a^{-8} - a^{-10} }[/math] |
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