K12a1171
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+3 q^5-6 q^4+10 q^3-13 q^2+16 q-17+16 q^{-1} -13 q^{-2} +10 q^{-3} -6 q^{-4} +3 q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-15 t^2+25 t-27+25 t^{-1} -15 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+9 z^4+z^2+1 }[/math] |
| Determinant | 115 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^6+z^6 a^{-2} +2 z^6-a^4 z^4+2 a^2 z^4+2 z^4 a^{-2} -z^4 a^{-4} +7 z^4-2 a^4 z^2-a^2 z^2-z^2 a^{-2} -2 z^2 a^{-4} +7 z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+3 a^4 z^{10}+10 a^2 z^{10}+7 z^{10}+a^5 z^9-5 a^3 z^9+6 a z^9+12 z^9 a^{-1} -18 a^4 z^8-50 a^2 z^8+14 z^8 a^{-2} -18 z^8-6 a^5 z^7-15 a^3 z^7-60 a z^7-38 z^7 a^{-1} +13 z^7 a^{-3} +37 a^4 z^6+76 a^2 z^6-38 z^6 a^{-2} +10 z^6 a^{-4} -9 z^6+13 a^5 z^5+54 a^3 z^5+103 a z^5+29 z^5 a^{-1} -27 z^5 a^{-3} +6 z^5 a^{-5} -30 a^4 z^4-35 a^2 z^4+24 z^4 a^{-2} -14 z^4 a^{-4} +3 z^4 a^{-6} +36 z^4-12 a^5 z^3-46 a^3 z^3-58 a z^3-9 z^3 a^{-1} +11 z^3 a^{-3} -3 z^3 a^{-5} +z^3 a^{-7} +8 a^4 z^2+a^2 z^2-7 z^2 a^{-2} +4 z^2 a^{-4} -18 z^2+4 a^5 z+11 a^3 z+10 a z+2 z a^{-1} -z a^{-3} +a^2+ a^{-2} +3 }[/math] |
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