K12a343
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-18 q^6+25 q^5-30 q^4+32 q^3-29 q^2+23 q-15+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-19 t^2+47 t-61+47 t^{-1} -19 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-z^4-2 z^2+1 }[/math] |
| Determinant | 199 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -z^4 a^{-2} +5 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-4 z^2 a^{-2} +7 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} -2 z^2+a^2-2 a^{-2} +4 a^{-4} -3 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +13 z^{10} a^{-4} +7 z^{10} a^{-6} +7 z^9 a^{-1} +14 z^9 a^{-3} +17 z^9 a^{-5} +10 z^9 a^{-7} -7 z^8 a^{-2} -23 z^8 a^{-4} -3 z^8 a^{-6} +8 z^8 a^{-8} +5 z^8+3 a z^7-14 z^7 a^{-1} -51 z^7 a^{-3} -57 z^7 a^{-5} -19 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-z^6 a^{-2} +3 z^6 a^{-4} -22 z^6 a^{-6} -16 z^6 a^{-8} +z^6 a^{-10} -8 z^6-7 a z^5+15 z^5 a^{-1} +73 z^5 a^{-3} +69 z^5 a^{-5} +10 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+10 z^4 a^{-2} +27 z^4 a^{-4} +31 z^4 a^{-6} +9 z^4 a^{-8} -2 z^4 a^{-10} +4 a z^3-14 z^3 a^{-1} -44 z^3 a^{-3} -35 z^3 a^{-5} -5 z^3 a^{-7} +4 z^3 a^{-9} +3 a^2 z^2-10 z^2 a^{-2} -19 z^2 a^{-4} -16 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} +2 z^2+4 z a^{-1} +9 z a^{-3} +7 z a^{-5} +z a^{-7} -z a^{-9} -a^2+2 a^{-2} +4 a^{-4} +3 a^{-6} + a^{-8} }[/math] |
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