K12a58
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-17 q^3+25 q^2-30 q+33-30 q^{-1} +25 q^{-2} -17 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+23 t^2-44 t+55-44 t^{-1} +23 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+z^4+z^2+1 }[/math] |
| Determinant | 205 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-7 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +13 z^4+2 a^4 z^2-10 a^2 z^2-10 z^2 a^{-2} +2 z^2 a^{-4} +17 z^2+a^4-5 a^2-5 a^{-2} + a^{-4} +9 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+4 z^{10} a^{-2} +8 z^{10}+7 a^3 z^9+17 a z^9+17 z^9 a^{-1} +7 z^9 a^{-3} +7 a^4 z^8+13 a^2 z^8+13 z^8 a^{-2} +7 z^8 a^{-4} +12 z^8+4 a^5 z^7-3 a^3 z^7-25 a z^7-25 z^7 a^{-1} -3 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-13 a^4 z^6-44 a^2 z^6-44 z^6 a^{-2} -13 z^6 a^{-4} +z^6 a^{-6} -60 z^6-9 a^5 z^5-18 a^3 z^5-10 a z^5-10 z^5 a^{-1} -18 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+8 a^4 z^4+43 a^2 z^4+43 z^4 a^{-2} +8 z^4 a^{-4} -2 z^4 a^{-6} +66 z^4+7 a^5 z^3+22 a^3 z^3+30 a z^3+30 z^3 a^{-1} +22 z^3 a^{-3} +7 z^3 a^{-5} +a^6 z^2-3 a^4 z^2-21 a^2 z^2-21 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} -34 z^2-2 a^5 z-8 a^3 z-13 a z-13 z a^{-1} -8 z a^{-3} -2 z a^{-5} +a^4+5 a^2+5 a^{-2} + a^{-4} +9 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
