K12a143
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{16}-3 q^{15}+5 q^{14}-8 q^{13}+10 q^{12}-12 q^{11}+12 q^{10}-11 q^9+9 q^8-6 q^7+5 q^6-2 q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^4-8 t^3+12 t^2-13 t+13-13 t^{-1} +12 t^{-2} -8 t^{-3} +3 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^8+16 z^6+24 z^4+11 z^2+1 }[/math] |
| Determinant | 85 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +2 z^8 a^{-10} +6 z^6 a^{-8} +13 z^6 a^{-10} -3 z^6 a^{-12} +11 z^4 a^{-8} +28 z^4 a^{-10} -16 z^4 a^{-12} +z^4 a^{-14} +7 z^2 a^{-8} +24 z^2 a^{-10} -24 z^2 a^{-12} +4 z^2 a^{-14} + a^{-8} +7 a^{-10} -10 a^{-12} +3 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +3 z^{10} a^{-10} +6 z^{10} a^{-12} +3 z^{10} a^{-14} +2 z^9 a^{-9} +z^9 a^{-11} +3 z^9 a^{-13} +4 z^9 a^{-15} +z^8 a^{-8} -17 z^8 a^{-10} -31 z^8 a^{-12} -9 z^8 a^{-14} +4 z^8 a^{-16} -10 z^7 a^{-9} -25 z^7 a^{-11} -30 z^7 a^{-13} -11 z^7 a^{-15} +4 z^7 a^{-17} -6 z^6 a^{-8} +34 z^6 a^{-10} +58 z^6 a^{-12} +8 z^6 a^{-14} -6 z^6 a^{-16} +4 z^6 a^{-18} +13 z^5 a^{-9} +53 z^5 a^{-11} +59 z^5 a^{-13} +13 z^5 a^{-15} -3 z^5 a^{-17} +3 z^5 a^{-19} +11 z^4 a^{-8} -38 z^4 a^{-10} -61 z^4 a^{-12} -4 z^4 a^{-14} +3 z^4 a^{-16} -4 z^4 a^{-18} +z^4 a^{-20} -4 z^3 a^{-9} -42 z^3 a^{-11} -48 z^3 a^{-13} -8 z^3 a^{-15} -2 z^3 a^{-17} -4 z^3 a^{-19} -7 z^2 a^{-8} +26 z^2 a^{-10} +38 z^2 a^{-12} +4 z^2 a^{-14} -z^2 a^{-20} +12 z a^{-11} +13 z a^{-13} +2 z a^{-15} +2 z a^{-17} +z a^{-19} + a^{-8} -7 a^{-10} -10 a^{-12} -3 a^{-14} }[/math] |
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