K12a311
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-17 q^9+23 q^8-28 q^7+31 q^6-27 q^5+22 q^4-15 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+23 t^2-42 t+49-42 t^{-1} +23 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-7 z^4+5 z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -9 z^4 a^{-6} +z^4 a^{-10} +2 z^2 a^{-2} +5 z^2 a^{-4} -7 z^2 a^{-6} +4 z^2 a^{-8} +z^2 a^{-10} +2 a^{-4} - a^{-6} + a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +6 z^{10} a^{-6} +12 z^{10} a^{-8} +6 z^{10} a^{-10} +8 z^9 a^{-5} +11 z^9 a^{-7} +11 z^9 a^{-9} +8 z^9 a^{-11} +6 z^8 a^{-4} -8 z^8 a^{-6} -26 z^8 a^{-8} -5 z^8 a^{-10} +7 z^8 a^{-12} +3 z^7 a^{-3} -21 z^7 a^{-5} -40 z^7 a^{-7} -32 z^7 a^{-9} -12 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -15 z^6 a^{-4} -2 z^6 a^{-6} +27 z^6 a^{-8} -z^6 a^{-10} -13 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +26 z^5 a^{-5} +56 z^5 a^{-7} +32 z^5 a^{-9} -9 z^5 a^{-13} -3 z^4 a^{-2} +14 z^4 a^{-4} +13 z^4 a^{-6} -16 z^4 a^{-8} -6 z^4 a^{-10} +4 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} -17 z^3 a^{-5} -32 z^3 a^{-7} -13 z^3 a^{-9} +5 z^3 a^{-11} +6 z^3 a^{-13} +2 z^2 a^{-2} -9 z^2 a^{-4} -7 z^2 a^{-6} +8 z^2 a^{-8} +4 z^2 a^{-10} +z^2 a^{-12} +z^2 a^{-14} +2 z a^{-5} +6 z a^{-7} -5 z a^{-11} -z a^{-13} +2 a^{-4} + a^{-6} + a^{-8} + a^{-10} }[/math] |
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