K12n369
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+6 q^5-10 q^4+12 q^3-12 q^2+12 q-9+6 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-9 t^2+15 t-17+15 t^{-1} -9 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-5 z^4-z^2+1 }[/math] |
| Determinant | 75 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +z^6-13 z^4 a^{-2} +4 z^4 a^{-4} +4 z^4-11 z^2 a^{-2} +5 z^2 a^{-4} +5 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +3 z^9 a^{-1} +5 z^9 a^{-3} +2 z^9 a^{-5} +4 z^8 a^{-2} +z^8 a^{-4} +z^8 a^{-6} +4 z^8+3 a z^7-5 z^7 a^{-1} -14 z^7 a^{-3} -6 z^7 a^{-5} +a^2 z^6-20 z^6 a^{-2} -9 z^6 a^{-4} -z^6 a^{-6} -11 z^6-9 a z^5-3 z^5 a^{-1} +14 z^5 a^{-3} +11 z^5 a^{-5} +3 z^5 a^{-7} -3 a^2 z^4+28 z^4 a^{-2} +19 z^4 a^{-4} +3 z^4 a^{-6} +z^4 a^{-8} +8 z^4+6 a z^3+4 z^3 a^{-1} -z^3 a^{-3} -4 z^3 a^{-5} -5 z^3 a^{-7} +2 a^2 z^2-17 z^2 a^{-2} -9 z^2 a^{-4} -2 z^2 a^{-6} -2 z^2 a^{-8} -6 z^2-a z-2 z a^{-1} -z a^{-3} +z a^{-5} +z a^{-7} +2 a^{-2} + a^{-4} +2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
