K12n33
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^6+7 q^5-12 q^4+17 q^3-20 q^2+20 q-18+14 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-16 t^2+25 t-27+25 t^{-1} -16 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6-z^2+1 }[/math] |
| Determinant | 123 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-10 z^4 a^{-2} +4 z^4 a^{-4} +7 z^4-2 a^2 z^2-11 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +7 z^2-5 a^{-2} +4 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+5 a z^9+13 z^9 a^{-1} +8 z^9 a^{-3} +4 a^2 z^8+17 z^8 a^{-2} +11 z^8 a^{-4} +10 z^8+a^3 z^7-12 a z^7-30 z^7 a^{-1} -11 z^7 a^{-3} +6 z^7 a^{-5} -14 a^2 z^6-64 z^6 a^{-2} -27 z^6 a^{-4} +z^6 a^{-6} -50 z^6-3 a^3 z^5+a z^5+6 z^5 a^{-1} -3 z^5 a^{-3} -5 z^5 a^{-5} +16 a^2 z^4+67 z^4 a^{-2} +36 z^4 a^{-4} +8 z^4 a^{-6} +55 z^4+3 a^3 z^3+9 a z^3+9 z^3 a^{-1} +6 z^3 a^{-3} +6 z^3 a^{-5} +3 z^3 a^{-7} -6 a^2 z^2-32 z^2 a^{-2} -22 z^2 a^{-4} -6 z^2 a^{-6} -22 z^2-a^3 z-3 a z-2 z a^{-1} -z a^{-3} -2 z a^{-5} -z a^{-7} +5 a^{-2} +4 a^{-4} + a^{-6} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
