K12a575
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-4 q^{14}+8 q^{13}-15 q^{12}+22 q^{11}-27 q^{10}+29 q^9-27 q^8+22 q^7-15 q^6+9 q^5-3 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^3-21 t^2+40 t-49+40 t^{-1} -21 t^{-2} +6 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^6+15 z^4+10 z^2+1 }[/math] |
| Determinant | 183 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +3 z^6 a^{-8} +2 z^6 a^{-10} +3 z^4 a^{-6} +10 z^4 a^{-8} +5 z^4 a^{-10} -3 z^4 a^{-12} +3 z^2 a^{-6} +9 z^2 a^{-8} +4 z^2 a^{-10} -7 z^2 a^{-12} +z^2 a^{-14} + a^{-6} + a^{-8} +2 a^{-10} -4 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +4 z^{10} a^{-10} +8 z^{10} a^{-12} +4 z^{10} a^{-14} +6 z^9 a^{-9} +13 z^9 a^{-11} +14 z^9 a^{-13} +7 z^9 a^{-15} +6 z^8 a^{-8} +3 z^8 a^{-10} -5 z^8 a^{-12} +5 z^8 a^{-14} +7 z^8 a^{-16} +3 z^7 a^{-7} -5 z^7 a^{-9} -26 z^7 a^{-11} -33 z^7 a^{-13} -11 z^7 a^{-15} +4 z^7 a^{-17} +z^6 a^{-6} -13 z^6 a^{-8} -11 z^6 a^{-10} -4 z^6 a^{-12} -25 z^6 a^{-14} -17 z^6 a^{-16} +z^6 a^{-18} -6 z^5 a^{-7} -8 z^5 a^{-9} +19 z^5 a^{-11} +32 z^5 a^{-13} +z^5 a^{-15} -10 z^5 a^{-17} -3 z^4 a^{-6} +12 z^4 a^{-8} -z^4 a^{-10} -6 z^4 a^{-12} +25 z^4 a^{-14} +13 z^4 a^{-16} -2 z^4 a^{-18} +3 z^3 a^{-7} +9 z^3 a^{-9} -11 z^3 a^{-11} -17 z^3 a^{-13} +6 z^3 a^{-15} +6 z^3 a^{-17} +3 z^2 a^{-6} -7 z^2 a^{-8} +6 z^2 a^{-10} +12 z^2 a^{-12} -7 z^2 a^{-14} -3 z^2 a^{-16} -2 z a^{-9} +4 z a^{-11} +4 z a^{-13} -2 z a^{-15} - a^{-6} + a^{-8} -2 a^{-10} -4 a^{-12} - a^{-14} }[/math] |
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