K12a546
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+11 q^7-20 q^6+28 q^5-35 q^4+37 q^3-34 q^2+28 q-18+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-21 t^2+55 t-73+55 t^{-1} -21 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-3 z^4-2 z^2+1 }[/math] |
| Determinant | 231 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -2 z^4 a^{-2} +4 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-5 z^2 a^{-2} +5 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} -2 a^{-2} +2 a^{-4} -2 a^{-6} + a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +7 z^{10} a^{-2} +14 z^{10} a^{-4} +7 z^{10} a^{-6} +10 z^9 a^{-1} +21 z^9 a^{-3} +22 z^9 a^{-5} +11 z^9 a^{-7} +2 z^8 a^{-2} -8 z^8 a^{-4} +7 z^8 a^{-6} +9 z^8 a^{-8} +8 z^8+4 a z^7-17 z^7 a^{-1} -53 z^7 a^{-3} -53 z^7 a^{-5} -17 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-28 z^6 a^{-2} -34 z^6 a^{-4} -42 z^6 a^{-6} -18 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5+11 z^5 a^{-1} +46 z^5 a^{-3} +41 z^5 a^{-5} +7 z^5 a^{-7} -7 z^5 a^{-9} -2 a^2 z^4+35 z^4 a^{-2} +47 z^4 a^{-4} +43 z^4 a^{-6} +15 z^4 a^{-8} -2 z^4 a^{-10} +12 z^4+4 a z^3-5 z^3 a^{-1} -18 z^3 a^{-3} -17 z^3 a^{-5} -4 z^3 a^{-7} +4 z^3 a^{-9} +a^2 z^2-18 z^2 a^{-2} -20 z^2 a^{-4} -18 z^2 a^{-6} -8 z^2 a^{-8} +z^2 a^{-10} -6 z^2+z a^{-1} +4 z a^{-3} +6 z a^{-5} +2 z a^{-7} -z a^{-9} +2 a^{-2} +2 a^{-4} +2 a^{-6} + a^{-8} +2 }[/math] |
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