K12a1175
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-19 q^6+27 q^5-33 q^4+36 q^3-33 q^2+27 q-18+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-26 t^2+46 t-55+46 t^{-1} -26 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-6 z^4+1 }[/math] |
| Determinant | 223 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-6 z^4 a^{-2} -6 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-3 z^2 a^{-2} -3 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +8 z^{10} a^{-2} +17 z^{10} a^{-4} +9 z^{10} a^{-6} +10 z^9 a^{-1} +14 z^9 a^{-3} +15 z^9 a^{-5} +11 z^9 a^{-7} -6 z^8 a^{-2} -35 z^8 a^{-4} -13 z^8 a^{-6} +8 z^8 a^{-8} +8 z^8+4 a z^7-17 z^7 a^{-1} -45 z^7 a^{-3} -51 z^7 a^{-5} -23 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-13 z^6 a^{-2} +27 z^6 a^{-4} +7 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5+6 z^5 a^{-1} +46 z^5 a^{-3} +61 z^5 a^{-5} +21 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+19 z^4 a^{-2} -7 z^4 a^{-4} -5 z^4 a^{-6} +7 z^4 a^{-8} -2 z^4 a^{-10} +10 z^4+4 a z^3+z^3 a^{-1} -17 z^3 a^{-3} -32 z^3 a^{-5} -14 z^3 a^{-7} +4 z^3 a^{-9} +a^2 z^2-7 z^2 a^{-2} +2 z^2 a^{-4} +z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} -5 z^2-a z-z a^{-1} +3 z a^{-3} +5 z a^{-5} +2 z a^{-7} +1 }[/math] |
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