K12a344
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-3 q^{14}+7 q^{13}-13 q^{12}+17 q^{11}-21 q^{10}+22 q^9-20 q^8+16 q^7-10 q^6+6 q^5-2 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^3-17 t^2+30 t-35+30 t^{-1} -17 t^{-2} +5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^6+13 z^4+7 z^2+1 }[/math] |
| Determinant | 139 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +2 z^6 a^{-8} +2 z^6 a^{-10} +4 z^4 a^{-6} +6 z^4 a^{-8} +6 z^4 a^{-10} -3 z^4 a^{-12} +5 z^2 a^{-6} +4 z^2 a^{-8} +5 z^2 a^{-10} -8 z^2 a^{-12} +z^2 a^{-14} +2 a^{-6} +2 a^{-10} -5 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +3 z^{10} a^{-10} +7 z^{10} a^{-12} +4 z^{10} a^{-14} +3 z^9 a^{-9} +6 z^9 a^{-11} +9 z^9 a^{-13} +6 z^9 a^{-15} +3 z^8 a^{-8} -6 z^8 a^{-10} -20 z^8 a^{-12} -6 z^8 a^{-14} +5 z^8 a^{-16} +2 z^7 a^{-7} -3 z^7 a^{-9} -24 z^7 a^{-11} -38 z^7 a^{-13} -16 z^7 a^{-15} +3 z^7 a^{-17} +z^6 a^{-6} -6 z^6 a^{-8} +13 z^6 a^{-10} +34 z^6 a^{-12} +z^6 a^{-14} -12 z^6 a^{-16} +z^6 a^{-18} -5 z^5 a^{-7} -3 z^5 a^{-9} +44 z^5 a^{-11} +69 z^5 a^{-13} +19 z^5 a^{-15} -8 z^5 a^{-17} -4 z^4 a^{-6} +2 z^4 a^{-8} -18 z^4 a^{-10} -31 z^4 a^{-12} +3 z^4 a^{-14} +7 z^4 a^{-16} -3 z^4 a^{-18} +2 z^3 a^{-7} +3 z^3 a^{-9} -34 z^3 a^{-11} -56 z^3 a^{-13} -16 z^3 a^{-15} +5 z^3 a^{-17} +5 z^2 a^{-6} +10 z^2 a^{-10} +19 z^2 a^{-12} -2 z^2 a^{-16} +2 z^2 a^{-18} +z a^{-7} -z a^{-9} +9 z a^{-11} +17 z a^{-13} +5 z a^{-15} -z a^{-17} -2 a^{-6} -2 a^{-10} -5 a^{-12} -2 a^{-14} }[/math] |
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