K12a1214
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{14}-2 q^{13}+3 q^{12}-4 q^{11}+5 q^{10}-6 q^9+5 q^8-6 q^7+5 q^6-3 q^5+3 q^4-q^3+q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+3 t^4-4 t^3+5 t^2-6 t+7-6 t^{-1} +5 t^{-2} -4 t^{-3} +3 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-7 z^8-15 z^6-9 z^4+z^2+1 }[/math] |
| Determinant | 45 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-8} +z^8 a^{-6} -9 z^8 a^{-8} +z^8 a^{-10} +8 z^6 a^{-6} -30 z^6 a^{-8} +7 z^6 a^{-10} +22 z^4 a^{-6} -47 z^4 a^{-8} +16 z^4 a^{-10} +24 z^2 a^{-6} -37 z^2 a^{-8} +14 z^2 a^{-10} +9 a^{-6} -13 a^{-8} +5 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +z^{10} a^{-6} +4 z^{10} a^{-8} +3 z^{10} a^{-10} -7 z^9 a^{-7} -3 z^9 a^{-9} +4 z^9 a^{-11} -9 z^8 a^{-6} -31 z^8 a^{-8} -17 z^8 a^{-10} +5 z^8 a^{-12} +14 z^7 a^{-7} -10 z^7 a^{-9} -18 z^7 a^{-11} +6 z^7 a^{-13} +30 z^6 a^{-6} +85 z^6 a^{-8} +30 z^6 a^{-10} -20 z^6 a^{-12} +5 z^6 a^{-14} -z^5 a^{-7} +43 z^5 a^{-9} +18 z^5 a^{-11} -22 z^5 a^{-13} +4 z^5 a^{-15} -46 z^4 a^{-6} -101 z^4 a^{-8} -22 z^4 a^{-10} +18 z^4 a^{-12} -12 z^4 a^{-14} +3 z^4 a^{-16} -19 z^3 a^{-7} -45 z^3 a^{-9} +2 z^3 a^{-11} +20 z^3 a^{-13} -6 z^3 a^{-15} +2 z^3 a^{-17} +33 z^2 a^{-6} +54 z^2 a^{-8} +13 z^2 a^{-10} -2 z^2 a^{-12} +3 z^2 a^{-14} -2 z^2 a^{-16} +z^2 a^{-18} +11 z a^{-7} +15 z a^{-9} -2 z a^{-11} -6 z a^{-13} -9 a^{-6} -13 a^{-8} -5 a^{-10} }[/math] |
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