K12a762
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-2 q^{12}+3 q^{11}-5 q^{10}+6 q^9-7 q^8+7 q^7-6 q^6+5 q^5-4 q^4+3 q^3-q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+6 t^3-7 t^2+7 t-7+7 t^{-1} -7 t^{-2} +6 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-10 z^6-11 z^4+z^2+1 }[/math] |
| Determinant | 51 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -6 z^6 a^{-6} -6 z^6 a^{-8} +z^6 a^{-10} +6 z^4 a^{-4} -11 z^4 a^{-6} -11 z^4 a^{-8} +5 z^4 a^{-10} +10 z^2 a^{-4} -8 z^2 a^{-6} -7 z^2 a^{-8} +6 z^2 a^{-10} +4 a^{-4} -3 a^{-6} - a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +z^{10} a^{-6} +3 z^{10} a^{-8} +2 z^{10} a^{-10} +z^9 a^{-5} -6 z^9 a^{-7} -5 z^9 a^{-9} +2 z^9 a^{-11} +z^8 a^{-4} -4 z^8 a^{-6} -18 z^8 a^{-8} -11 z^8 a^{-10} +2 z^8 a^{-12} -5 z^7 a^{-5} +15 z^7 a^{-7} +10 z^7 a^{-9} -8 z^7 a^{-11} +2 z^7 a^{-13} -7 z^6 a^{-4} +39 z^6 a^{-8} +24 z^6 a^{-10} -6 z^6 a^{-12} +2 z^6 a^{-14} +5 z^5 a^{-5} -24 z^5 a^{-7} -11 z^5 a^{-9} +12 z^5 a^{-11} -4 z^5 a^{-13} +2 z^5 a^{-15} +16 z^4 a^{-4} +11 z^4 a^{-6} -40 z^4 a^{-8} -23 z^4 a^{-10} +8 z^4 a^{-12} -3 z^4 a^{-14} +z^4 a^{-16} +3 z^3 a^{-5} +18 z^3 a^{-7} +3 z^3 a^{-9} -4 z^3 a^{-11} +4 z^3 a^{-13} -4 z^3 a^{-15} -14 z^2 a^{-4} -10 z^2 a^{-6} +15 z^2 a^{-8} +7 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} -2 z^2 a^{-16} -3 z a^{-5} -3 z a^{-7} -z a^{-11} +z a^{-15} +4 a^{-4} +3 a^{-6} - a^{-8} - a^{-10} }[/math] |
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