K12n292
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-2 q^{14}+2 q^{13}-2 q^{12}+q^{11}-q^{10}-q^9+2 q^8-2 q^7+3 q^6-q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-4 t^3+2 t^2+4 t-7+4 t^{-1} +2 t^{-2} -4 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+12 z^6+18 z^4+8 z^2+1 }[/math] |
| Determinant | 1 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +z^8 a^{-10} +7 z^6 a^{-8} +6 z^6 a^{-10} -z^6 a^{-12} +16 z^4 a^{-8} +9 z^4 a^{-10} -7 z^4 a^{-12} +15 z^2 a^{-8} +2 z^2 a^{-10} -11 z^2 a^{-12} +2 z^2 a^{-14} +5 a^{-8} -2 a^{-10} -4 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +3 z^9 a^{-11} +2 z^9 a^{-13} +z^8 a^{-8} -5 z^8 a^{-10} -6 z^8 a^{-12} +z^8 a^{-14} +z^8 a^{-16} -5 z^7 a^{-9} -19 z^7 a^{-11} -15 z^7 a^{-13} +z^7 a^{-15} +2 z^7 a^{-17} -7 z^6 a^{-8} +4 z^6 a^{-10} +9 z^6 a^{-12} -7 z^6 a^{-14} -4 z^6 a^{-16} +z^6 a^{-18} +4 z^5 a^{-9} +33 z^5 a^{-11} +33 z^5 a^{-13} -5 z^5 a^{-15} -9 z^5 a^{-17} +16 z^4 a^{-8} +4 z^4 a^{-10} -9 z^4 a^{-12} +9 z^4 a^{-14} +2 z^4 a^{-16} -4 z^4 a^{-18} +5 z^3 a^{-9} -19 z^3 a^{-11} -31 z^3 a^{-13} +2 z^3 a^{-15} +9 z^3 a^{-17} -15 z^2 a^{-8} -5 z^2 a^{-10} +11 z^2 a^{-12} -2 z^2 a^{-14} +3 z^2 a^{-18} -5 z a^{-9} +3 z a^{-11} +11 z a^{-13} +z a^{-15} -2 z a^{-17} +5 a^{-8} +2 a^{-10} -4 a^{-12} -2 a^{-14} }[/math] |
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