K12a828
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-4 q^{14}+10 q^{13}-18 q^{12}+24 q^{11}-30 q^{10}+31 q^9-28 q^8+23 q^7-14 q^6+8 q^5-3 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 7 t^3-24 t^2+42 t-49+42 t^{-1} -24 t^{-2} +7 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 7 z^6+18 z^4+9 z^2+1 }[/math] |
| Determinant | 195 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +3 z^6 a^{-8} +3 z^6 a^{-10} +3 z^4 a^{-6} +10 z^4 a^{-8} +9 z^4 a^{-10} -4 z^4 a^{-12} +2 z^2 a^{-6} +10 z^2 a^{-8} +6 z^2 a^{-10} -10 z^2 a^{-12} +z^2 a^{-14} +4 a^{-8} -5 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-11} +2 z^{11} a^{-13} +6 z^{10} a^{-10} +13 z^{10} a^{-12} +7 z^{10} a^{-14} +7 z^9 a^{-9} +13 z^9 a^{-11} +16 z^9 a^{-13} +10 z^9 a^{-15} +6 z^8 a^{-8} -8 z^8 a^{-10} -27 z^8 a^{-12} -5 z^8 a^{-14} +8 z^8 a^{-16} +3 z^7 a^{-7} -14 z^7 a^{-9} -49 z^7 a^{-11} -56 z^7 a^{-13} -20 z^7 a^{-15} +4 z^7 a^{-17} +z^6 a^{-6} -16 z^6 a^{-8} -z^6 a^{-10} +19 z^6 a^{-12} -14 z^6 a^{-14} -16 z^6 a^{-16} +z^6 a^{-18} -7 z^5 a^{-7} +9 z^5 a^{-9} +70 z^5 a^{-11} +75 z^5 a^{-13} +13 z^5 a^{-15} -8 z^5 a^{-17} -3 z^4 a^{-6} +18 z^4 a^{-8} +12 z^4 a^{-10} -z^4 a^{-12} +18 z^4 a^{-14} +8 z^4 a^{-16} -2 z^4 a^{-18} +3 z^3 a^{-7} -z^3 a^{-9} -41 z^3 a^{-11} -50 z^3 a^{-13} -9 z^3 a^{-15} +4 z^3 a^{-17} +2 z^2 a^{-6} -14 z^2 a^{-8} -8 z^2 a^{-10} +6 z^2 a^{-12} -6 z^2 a^{-14} -3 z^2 a^{-16} +z^2 a^{-18} -2 z a^{-9} +10 z a^{-11} +16 z a^{-13} +3 z a^{-15} -z a^{-17} +4 a^{-8} -5 a^{-12} -2 a^{-14} }[/math] |
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