K12a232
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-16 q^9+23 q^8-28 q^7+29 q^6-27 q^5+22 q^4-14 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+20 t^2-42 t+53-42 t^{-1} +20 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-4 z^4+2 z^2+1 }[/math] |
| Determinant | 185 |
| 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} -4 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-10} + a^{-2} + a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +7 z^{10} a^{-8} +4 z^{10} a^{-10} +5 z^9 a^{-5} +11 z^9 a^{-7} +13 z^9 a^{-9} +7 z^9 a^{-11} +5 z^8 a^{-4} +9 z^8 a^{-6} +4 z^8 a^{-8} +7 z^8 a^{-10} +7 z^8 a^{-12} +3 z^7 a^{-3} -2 z^7 a^{-5} -13 z^7 a^{-7} -19 z^7 a^{-9} -7 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -9 z^6 a^{-4} -28 z^6 a^{-6} -28 z^6 a^{-8} -25 z^6 a^{-10} -14 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} -11 z^5 a^{-5} -10 z^5 a^{-7} -4 z^5 a^{-9} -7 z^5 a^{-11} -9 z^5 a^{-13} -3 z^4 a^{-2} +5 z^4 a^{-4} +25 z^4 a^{-6} +24 z^4 a^{-8} +17 z^4 a^{-10} +8 z^4 a^{-12} -2 z^4 a^{-14} +5 z^3 a^{-3} +13 z^3 a^{-5} +18 z^3 a^{-7} +13 z^3 a^{-9} +9 z^3 a^{-11} +6 z^3 a^{-13} +3 z^2 a^{-2} -2 z^2 a^{-4} -9 z^2 a^{-6} -6 z^2 a^{-8} -4 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} -z a^{-3} -5 z a^{-5} -6 z a^{-7} -4 z a^{-9} -3 z a^{-11} -z a^{-13} - a^{-2} + a^{-4} + a^{-6} }[/math] |
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