K12a722
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{14}-2 q^{13}+2 q^{12}-3 q^{11}+3 q^{10}-3 q^9+3 q^8-3 q^7+3 q^6-2 q^5+2 q^4-q^3+q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+3 t^4-3 t^3+3 t^2-3 t+3-3 t^{-1} +3 t^{-2} -3 t^{-3} +3 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-7 z^8-14 z^6-5 z^4+5 z^2+1 }[/math] |
| Determinant | 29 |
| 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} -29 z^6 a^{-8} +7 z^6 a^{-10} +21 z^4 a^{-6} -41 z^4 a^{-8} +15 z^4 a^{-10} +20 z^2 a^{-6} -25 z^2 a^{-8} +10 z^2 a^{-10} +5 a^{-6} -5 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +z^{10} a^{-6} +3 z^{10} a^{-8} +2 z^{10} a^{-10} -8 z^9 a^{-7} -6 z^9 a^{-9} +2 z^9 a^{-11} -9 z^8 a^{-6} -24 z^8 a^{-8} -13 z^8 a^{-10} +2 z^8 a^{-12} +21 z^7 a^{-7} +9 z^7 a^{-9} -10 z^7 a^{-11} +2 z^7 a^{-13} +29 z^6 a^{-6} +66 z^6 a^{-8} +27 z^6 a^{-10} -8 z^6 a^{-12} +2 z^6 a^{-14} -19 z^5 a^{-7} +z^5 a^{-9} +12 z^5 a^{-11} -6 z^5 a^{-13} +2 z^5 a^{-15} -41 z^4 a^{-6} -75 z^4 a^{-8} -22 z^4 a^{-10} +6 z^4 a^{-12} -4 z^4 a^{-14} +2 z^4 a^{-16} +z^3 a^{-7} -6 z^3 a^{-9} -z^3 a^{-11} +2 z^3 a^{-13} -2 z^3 a^{-15} +2 z^3 a^{-17} +25 z^2 a^{-6} +34 z^2 a^{-8} +8 z^2 a^{-10} +z^2 a^{-12} -z^2 a^{-16} +z^2 a^{-18} +3 z a^{-7} +z a^{-9} -z a^{-11} +z a^{-13} -z a^{-15} -z a^{-17} -5 a^{-6} -5 a^{-8} - a^{-10} }[/math] |
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