K12a1194
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-4 q^4+9 q^3-15 q^2+21 q-25+27 q^{-1} -25 q^{-2} +21 q^{-3} -14 q^{-4} +8 q^{-5} -4 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-23 t^2+34 t-37+34 t^{-1} -23 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-3 z^4+1 }[/math] |
| Determinant | 175 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-4 a^2 z^6+z^6 a^{-2} -4 z^6+3 a^4 z^4-4 a^2 z^4+3 z^4 a^{-2} -5 z^4+a^4 z^2+a^2 z^2+2 z^2 a^{-2} -4 z^2-a^4+3 a^2+ a^{-2} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +10 a^2 z^{10}+6 z^{10} a^{-2} +16 z^{10}+16 a^3 z^9+14 a z^9+2 z^9 a^{-1} +4 z^9 a^{-3} +16 a^4 z^8-15 a^2 z^8-23 z^8 a^{-2} +z^8 a^{-4} -55 z^8+12 a^5 z^7-39 a^3 z^7-78 a z^7-44 z^7 a^{-1} -17 z^7 a^{-3} +8 a^6 z^6-31 a^4 z^6-21 a^2 z^6+24 z^6 a^{-2} -4 z^6 a^{-4} +46 z^6+4 a^7 z^5-13 a^5 z^5+30 a^3 z^5+93 a z^5+69 z^5 a^{-1} +23 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+18 a^4 z^4+32 a^2 z^4-6 z^4 a^{-2} +5 z^4 a^{-4} -4 z^4-2 a^7 z^3-12 a^3 z^3-37 a z^3-35 z^3 a^{-1} -12 z^3 a^{-3} -3 a^4 z^2-4 a^2 z^2-z^2 a^{-2} -2 z^2 a^{-4} +a^5 z+3 a^3 z+5 a z+5 z a^{-1} +2 z a^{-3} -a^4-3 a^2- a^{-2} -2 }[/math] |
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