K12a822
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-3 q^{12}+7 q^{11}-12 q^{10}+15 q^9-18 q^8+18 q^7-16 q^6+13 q^5-8 q^4+5 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-15 t^2+22 t-25+22 t^{-1} -15 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-7 z^4+2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -7 z^4 a^{-6} -9 z^4 a^{-8} +4 z^4 a^{-10} +7 z^2 a^{-4} -z^2 a^{-6} -9 z^2 a^{-8} +5 z^2 a^{-10} +2 a^{-4} +2 a^{-6} -5 a^{-8} +2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +6 z^{10} a^{-8} +4 z^{10} a^{-10} +2 z^9 a^{-5} +z^9 a^{-7} +6 z^9 a^{-9} +7 z^9 a^{-11} +z^8 a^{-4} -7 z^8 a^{-6} -23 z^8 a^{-8} -6 z^8 a^{-10} +9 z^8 a^{-12} -10 z^7 a^{-5} -16 z^7 a^{-7} -27 z^7 a^{-9} -12 z^7 a^{-11} +9 z^7 a^{-13} -6 z^6 a^{-4} +4 z^6 a^{-6} +36 z^6 a^{-8} +5 z^6 a^{-10} -15 z^6 a^{-12} +6 z^6 a^{-14} +15 z^5 a^{-5} +27 z^5 a^{-7} +36 z^5 a^{-9} +6 z^5 a^{-11} -15 z^5 a^{-13} +3 z^5 a^{-15} +12 z^4 a^{-4} +3 z^4 a^{-6} -39 z^4 a^{-8} -15 z^4 a^{-10} +8 z^4 a^{-12} -6 z^4 a^{-14} +z^4 a^{-16} -6 z^3 a^{-5} -19 z^3 a^{-7} -30 z^3 a^{-9} -2 z^3 a^{-11} +13 z^3 a^{-13} -2 z^3 a^{-15} -9 z^2 a^{-4} +2 z^2 a^{-6} +23 z^2 a^{-8} +9 z^2 a^{-10} +z^2 a^{-12} +3 z^2 a^{-14} -z^2 a^{-16} +7 z a^{-7} +9 z a^{-9} -z a^{-11} -3 z a^{-13} +2 a^{-4} -2 a^{-6} -5 a^{-8} -2 a^{-10} }[/math] |
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