K12a920
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+6 q^8-11 q^7+15 q^6-18 q^5+19 q^4-17 q^3+15 q^2-10 q+6-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+4 t^4-9 t^3+16 t^2-21 t+23-21 t^{-1} +16 t^{-2} -9 t^{-3} +4 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-6 z^8-12 z^6-8 z^4+z^2+1 }[/math] |
| Determinant | 125 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -8 z^8 a^{-4} +z^8 a^{-6} +6 z^6 a^{-2} -24 z^6 a^{-4} +6 z^6 a^{-6} +12 z^4 a^{-2} -32 z^4 a^{-4} +12 z^4 a^{-6} +9 z^2 a^{-2} -16 z^2 a^{-4} +8 z^2 a^{-6} +2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +9 z^{10} a^{-4} +5 z^{10} a^{-6} +3 z^9 a^{-1} -3 z^9 a^{-3} +z^9 a^{-5} +7 z^9 a^{-7} -19 z^8 a^{-2} -38 z^8 a^{-4} -10 z^8 a^{-6} +8 z^8 a^{-8} +z^8-15 z^7 a^{-1} -12 z^7 a^{-3} -16 z^7 a^{-5} -12 z^7 a^{-7} +7 z^7 a^{-9} +30 z^6 a^{-2} +59 z^6 a^{-4} +6 z^6 a^{-6} -13 z^6 a^{-8} +5 z^6 a^{-10} -5 z^6+23 z^5 a^{-1} +24 z^5 a^{-3} +14 z^5 a^{-5} +2 z^5 a^{-7} -8 z^5 a^{-9} +3 z^5 a^{-11} -22 z^4 a^{-2} -51 z^4 a^{-4} -10 z^4 a^{-6} +7 z^4 a^{-8} -4 z^4 a^{-10} +z^4 a^{-12} +7 z^4-11 z^3 a^{-1} -13 z^3 a^{-3} -4 z^3 a^{-5} +4 z^3 a^{-7} +3 z^3 a^{-9} -3 z^3 a^{-11} +10 z^2 a^{-2} +20 z^2 a^{-4} +6 z^2 a^{-6} +z^2 a^{-10} -z^2 a^{-12} -2 z^2+z a^{-1} +2 z a^{-3} -z a^{-5} -2 z a^{-7} +z a^{-9} +z a^{-11} -2 a^{-2} - a^{-4} }[/math] |
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