K12n225
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+5 q^7-7 q^6+8 q^5-7 q^4+6 q^3-4 q^2+q+1- q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^2+10 t-13+10 t^{-1} -3 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^4-2 z^2+1 }[/math] |
| Determinant | 39 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} +z^6 a^{-4} -7 z^4 a^{-2} +5 z^4 a^{-4} -2 z^4 a^{-6} +z^4-13 z^2 a^{-2} +11 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +4 z^2-8 a^{-2} +8 a^{-4} -4 a^{-6} + a^{-8} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^9 a^{-1} +z^9 a^{-3} +z^9 a^{-5} +z^9 a^{-7} +2 z^8 a^{-2} +3 z^8 a^{-4} +5 z^8 a^{-6} +3 z^8 a^{-8} +z^8-7 z^7 a^{-1} -8 z^7 a^{-3} -z^7 a^{-5} +3 z^7 a^{-7} +3 z^7 a^{-9} -18 z^6 a^{-2} -20 z^6 a^{-4} -18 z^6 a^{-6} -8 z^6 a^{-8} +z^6 a^{-10} -7 z^6+13 z^5 a^{-1} +15 z^5 a^{-3} -6 z^5 a^{-5} -18 z^5 a^{-7} -10 z^5 a^{-9} +43 z^4 a^{-2} +45 z^4 a^{-4} +23 z^4 a^{-6} +3 z^4 a^{-8} -3 z^4 a^{-10} +15 z^4-8 z^3 a^{-1} -3 z^3 a^{-3} +13 z^3 a^{-5} +16 z^3 a^{-7} +8 z^3 a^{-9} -34 z^2 a^{-2} -33 z^2 a^{-4} -16 z^2 a^{-6} -2 z^2 a^{-8} +2 z^2 a^{-10} -13 z^2+z a^{-1} -z a^{-3} -5 z a^{-5} -5 z a^{-7} -2 z a^{-9} +8 a^{-2} +8 a^{-4} +4 a^{-6} + a^{-8} +4 }[/math] |
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