K12a1233
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-2 q^9+4 q^8-7 q^7+9 q^6-11 q^5+11 q^4-10 q^3+9 q^2-6 q+4-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+3 t^4-6 t^3+10 t^2-12 t+13-12 t^{-1} +10 t^{-2} -6 t^{-3} +3 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-7 z^8-17 z^6-16 z^4-3 z^2+1 }[/math] |
| Determinant | 77 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -9 z^8 a^{-4} +z^8 a^{-6} +7 z^6 a^{-2} -31 z^6 a^{-4} +7 z^6 a^{-6} +17 z^4 a^{-2} -50 z^4 a^{-4} +17 z^4 a^{-6} +17 z^2 a^{-2} -36 z^2 a^{-4} +16 z^2 a^{-6} +6 a^{-2} -9 a^{-4} +4 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10} a^{-6} +2 z^9 a^{-1} -2 z^9 a^{-3} +4 z^9 a^{-7} -10 z^8 a^{-2} -28 z^8 a^{-4} -13 z^8 a^{-6} +4 z^8 a^{-8} +z^8-11 z^7 a^{-1} -6 z^7 a^{-3} -14 z^7 a^{-5} -15 z^7 a^{-7} +4 z^7 a^{-9} +17 z^6 a^{-2} +64 z^6 a^{-4} +27 z^6 a^{-6} -11 z^6 a^{-8} +3 z^6 a^{-10} -6 z^6+18 z^5 a^{-1} +15 z^5 a^{-3} +34 z^5 a^{-5} +25 z^5 a^{-7} -10 z^5 a^{-9} +2 z^5 a^{-11} -19 z^4 a^{-2} -81 z^4 a^{-4} -32 z^4 a^{-6} +13 z^4 a^{-8} -5 z^4 a^{-10} +z^4 a^{-12} +11 z^4-9 z^3 a^{-1} -13 z^3 a^{-3} -36 z^3 a^{-5} -17 z^3 a^{-7} +12 z^3 a^{-9} -3 z^3 a^{-11} +18 z^2 a^{-2} +47 z^2 a^{-4} +16 z^2 a^{-6} -2 z^2 a^{-8} +3 z^2 a^{-10} -2 z^2 a^{-12} -6 z^2+z a^{-1} +6 z a^{-3} +10 z a^{-5} +3 z a^{-7} -2 z a^{-9} -6 a^{-2} -9 a^{-4} -4 a^{-6} }[/math] |
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