K12a730
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+7 q^{10}-13 q^9+18 q^8-23 q^7+24 q^6-22 q^5+19 q^4-12 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+18 t^2-34 t+41-34 t^{-1} +18 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-6 z^4+2 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -5 z^4 a^{-6} -2 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +3 z^2 a^{-4} -3 z^2 a^{-6} -2 z^2 a^{-8} +2 z^2 a^{-10} +3 a^{-4} - a^{-6} -2 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +6 z^{10} a^{-8} +3 z^{10} a^{-10} +5 z^9 a^{-5} +7 z^9 a^{-7} +7 z^9 a^{-9} +5 z^9 a^{-11} +5 z^8 a^{-4} +2 z^8 a^{-6} -6 z^8 a^{-8} +2 z^8 a^{-10} +5 z^8 a^{-12} +3 z^7 a^{-3} -9 z^7 a^{-5} -15 z^7 a^{-7} -14 z^7 a^{-9} -8 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -13 z^6 a^{-4} -16 z^6 a^{-6} -2 z^6 a^{-8} -13 z^6 a^{-10} -12 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +5 z^5 a^{-5} +13 z^5 a^{-7} +10 z^5 a^{-9} +2 z^5 a^{-11} -8 z^5 a^{-13} -3 z^4 a^{-2} +13 z^4 a^{-4} +23 z^4 a^{-6} +7 z^4 a^{-8} +12 z^4 a^{-10} +9 z^4 a^{-12} -3 z^4 a^{-14} +5 z^3 a^{-3} -z^3 a^{-5} -7 z^3 a^{-7} -6 z^3 a^{-9} +z^3 a^{-11} +6 z^3 a^{-13} +2 z^2 a^{-2} -9 z^2 a^{-4} -14 z^2 a^{-6} -z^2 a^{-8} -3 z^2 a^{-10} -3 z^2 a^{-12} +2 z^2 a^{-14} -z a^{-5} +3 z a^{-7} +5 z a^{-9} -z a^{-11} -2 z a^{-13} +3 a^{-4} + a^{-6} -2 a^{-8} - a^{-10} }[/math] |
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