K12n431
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+8 q^4-12 q^3+16 q^2-17 q+16-13 q^{-1} +9 q^{-2} -4 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+8 t^2-24 t+35-24 t^{-1} +8 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+2 z^4-z^2+1 }[/math] |
| Determinant | 101 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -3 z^4 a^{-2} +z^4 a^{-4} +4 z^4-4 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} +8 z^2+a^4-3 a^2-3 a^{-2} + a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+4 a z^9+10 z^9 a^{-1} +6 z^9 a^{-3} +2 a^2 z^8+6 z^8 a^{-2} +7 z^8 a^{-4} +z^8-14 a z^7-32 z^7 a^{-1} -14 z^7 a^{-3} +4 z^7 a^{-5} -4 a^2 z^6-32 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} -15 z^6+4 a^3 z^5+31 a z^5+44 z^5 a^{-1} +7 z^5 a^{-3} -10 z^5 a^{-5} +a^4 z^4+13 a^2 z^4+40 z^4 a^{-2} +15 z^4 a^{-4} -2 z^4 a^{-6} +35 z^4-5 a^3 z^3-24 a z^3-26 z^3 a^{-1} -3 z^3 a^{-3} +4 z^3 a^{-5} -2 a^4 z^2-13 a^2 z^2-19 z^2 a^{-2} -5 z^2 a^{-4} -25 z^2+2 a^3 z+5 a z+5 z a^{-1} +2 z a^{-3} +a^4+3 a^2+3 a^{-2} + a^{-4} +5 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
