K12a909
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+6 q^8-9 q^7+12 q^6-15 q^5+15 q^4-14 q^3+12 q^2-8 q+6-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+4 t^4-9 t^3+14 t^2-16 t+17-16 t^{-1} +14 t^{-2} -9 t^{-3} +4 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-6 z^8-12 z^6-10 z^4-2 z^2+1 }[/math] |
| Determinant | 105 |
| 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} -34 z^4 a^{-4} +12 z^4 a^{-6} +11 z^2 a^{-2} -23 z^2 a^{-4} +10 z^2 a^{-6} +5 a^{-2} -7 a^{-4} +3 a^{-6} }[/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} -4 z^9 a^{-3} -z^9 a^{-5} +6 z^9 a^{-7} -20 z^8 a^{-2} -45 z^8 a^{-4} -18 z^8 a^{-6} +6 z^8 a^{-8} +z^8-15 z^7 a^{-1} -13 z^7 a^{-3} -21 z^7 a^{-5} -17 z^7 a^{-7} +6 z^7 a^{-9} +31 z^6 a^{-2} +79 z^6 a^{-4} +27 z^6 a^{-6} -11 z^6 a^{-8} +5 z^6 a^{-10} -5 z^6+21 z^5 a^{-1} +31 z^5 a^{-3} +43 z^5 a^{-5} +21 z^5 a^{-7} -9 z^5 a^{-9} +3 z^5 a^{-11} -23 z^4 a^{-2} -70 z^4 a^{-4} -25 z^4 a^{-6} +8 z^4 a^{-8} -6 z^4 a^{-10} +z^4 a^{-12} +7 z^4-9 z^3 a^{-1} -20 z^3 a^{-3} -35 z^3 a^{-5} -15 z^3 a^{-7} +6 z^3 a^{-9} -3 z^3 a^{-11} +14 z^2 a^{-2} +33 z^2 a^{-4} +11 z^2 a^{-6} -2 z^2 a^{-8} +2 z^2 a^{-10} -z^2 a^{-12} -3 z^2+z a^{-1} +6 z a^{-3} +10 z a^{-5} +4 z a^{-7} -z a^{-9} -5 a^{-2} -7 a^{-4} -3 a^{-6} }[/math] |
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