K12n159
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+3 q^{-1} -5 q^{-2} +8 q^{-3} -8 q^{-4} +9 q^{-5} -8 q^{-6} +6 q^{-7} -4 q^{-8} +2 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-6 t^2+12 t-15+12 t^{-1} -6 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+6 z^4+6 z^2+1 }[/math] |
| Determinant | 55 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-3 z^2 a^8-2 a^8+z^6 a^6+4 z^4 a^6+5 z^2 a^6+a^6+z^6 a^4+4 z^4 a^4+6 z^2 a^4+3 a^4-z^4 a^2-2 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-5 z^5 a^{11}+7 z^3 a^{11}-3 z a^{11}+2 z^8 a^{10}-9 z^6 a^{10}+11 z^4 a^{10}-4 z^2 a^{10}+2 z^9 a^9-7 z^7 a^9+4 z^5 a^9+z^3 a^9+z^{10} a^8-z^8 a^8-6 z^6 a^8+5 z^4 a^8+2 z^2 a^8-2 a^8+4 z^9 a^7-15 z^7 a^7+18 z^5 a^7-12 z^3 a^7+3 z a^7+z^{10} a^6-z^8 a^6-3 z^6 a^6+3 z^4 a^6-a^6+2 z^9 a^5-6 z^7 a^5+8 z^5 a^5-3 z^3 a^5-z a^5+2 z^8 a^4-6 z^6 a^4+12 z^4 a^4-9 z^2 a^4+3 a^4+z^7 a^3-z^5 a^3+4 z^3 a^3-2 z a^3+3 z^4 a^2-3 z^2 a^2+a^2+z^3 a-z a }[/math] |
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