K12a281
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+5 q^{10}-11 q^9+18 q^8-27 q^7+32 q^6-33 q^5+31 q^4-24 q^3+17 q^2-9 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+24 t^2-46 t+57-46 t^{-1} +24 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+2 z^4+3 z^2+1 }[/math] |
| Determinant | 213 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +5 z^6 a^{-4} -3 z^6 a^{-6} -3 z^4 a^{-2} +12 z^4 a^{-4} -10 z^4 a^{-6} +3 z^4 a^{-8} -3 z^2 a^{-2} +14 z^2 a^{-4} -12 z^2 a^{-6} +5 z^2 a^{-8} -z^2 a^{-10} - a^{-2} +6 a^{-4} -5 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-5} +z^{11} a^{-7} +4 z^{10} a^{-4} +9 z^{10} a^{-6} +5 z^{10} a^{-8} +6 z^9 a^{-3} +18 z^9 a^{-5} +23 z^9 a^{-7} +11 z^9 a^{-9} +4 z^8 a^{-2} +6 z^8 a^{-4} +11 z^8 a^{-6} +23 z^8 a^{-8} +14 z^8 a^{-10} +z^7 a^{-1} -14 z^7 a^{-3} -45 z^7 a^{-5} -39 z^7 a^{-7} +2 z^7 a^{-9} +11 z^7 a^{-11} -13 z^6 a^{-2} -45 z^6 a^{-4} -77 z^6 a^{-6} -66 z^6 a^{-8} -16 z^6 a^{-10} +5 z^6 a^{-12} -3 z^5 a^{-1} +5 z^5 a^{-3} +18 z^5 a^{-5} -6 z^5 a^{-7} -31 z^5 a^{-9} -14 z^5 a^{-11} +z^5 a^{-13} +15 z^4 a^{-2} +57 z^4 a^{-4} +83 z^4 a^{-6} +50 z^4 a^{-8} +5 z^4 a^{-10} -4 z^4 a^{-12} +3 z^3 a^{-1} +7 z^3 a^{-3} +16 z^3 a^{-5} +28 z^3 a^{-7} +22 z^3 a^{-9} +6 z^3 a^{-11} -7 z^2 a^{-2} -28 z^2 a^{-4} -33 z^2 a^{-6} -14 z^2 a^{-8} -2 z^2 a^{-10} -z a^{-1} -4 z a^{-3} -10 z a^{-5} -9 z a^{-7} -2 z a^{-9} + a^{-2} +6 a^{-4} +5 a^{-6} + a^{-8} }[/math] |
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