K12n172
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+q^9-2 q^8+3 q^7-3 q^6+4 q^5-3 q^4+3 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-6 t^2+t+3+ t^{-1} -6 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6+4 z^4+6 z^2+1 }[/math] |
| Determinant | 23 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} +z^6 a^{-4} -6 z^6 a^{-6} +2 z^6 a^{-8} +5 z^4 a^{-4} -11 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} +6 z^2 a^{-4} -9 z^2 a^{-6} +15 z^2 a^{-8} -6 z^2 a^{-10} +2 a^{-4} -3 a^{-6} +6 a^{-8} -5 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +4 z^9 a^{-7} +2 z^9 a^{-9} +z^8 a^{-4} -3 z^8 a^{-6} -2 z^8 a^{-8} +2 z^8 a^{-10} -12 z^7 a^{-5} -23 z^7 a^{-7} -10 z^7 a^{-9} +z^7 a^{-11} -6 z^6 a^{-4} -7 z^6 a^{-6} -13 z^6 a^{-8} -12 z^6 a^{-10} +21 z^5 a^{-5} +37 z^5 a^{-7} +10 z^5 a^{-9} -6 z^5 a^{-11} +11 z^4 a^{-4} +23 z^4 a^{-6} +33 z^4 a^{-8} +21 z^4 a^{-10} -12 z^3 a^{-5} -20 z^3 a^{-7} +z^3 a^{-9} +9 z^3 a^{-11} -8 z^2 a^{-4} -16 z^2 a^{-6} -24 z^2 a^{-8} -17 z^2 a^{-10} -z^2 a^{-12} +z a^{-5} +3 z a^{-7} -3 z a^{-9} -5 z a^{-11} +2 a^{-4} +3 a^{-6} +6 a^{-8} +5 a^{-10} + a^{-12} }[/math] |
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