K12n685
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+4 q^{-1} -7 q^{-2} +11 q^{-3} -12 q^{-4} +13 q^{-5} -12 q^{-6} +9 q^{-7} -6 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-8 t^2+18 t-23+18 t^{-1} -8 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+4 z^4+4 z^2+1 }[/math] |
| Determinant | 79 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+3 z^4 a^6+3 z^2 a^6+z^6 a^4+3 z^4 a^4+4 z^2 a^4+2 a^4-z^4 a^2-z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-12 z^6 a^{10}+14 z^4 a^{10}-4 z^2 a^{10}+3 z^9 a^9-8 z^7 a^9+8 z^3 a^9-2 z a^9+z^{10} a^8+4 z^8 a^8-20 z^6 a^8+15 z^4 a^8-a^8+5 z^9 a^7-9 z^7 a^7-5 z^5 a^7+7 z^3 a^7-2 z a^7+z^{10} a^6+3 z^8 a^6-7 z^6 a^6-4 z^4 a^6+3 z^2 a^6+2 z^9 a^5+z^7 a^5-6 z^5 a^5+3 z^3 a^5-2 z a^5+2 z^8 a^4+z^6 a^4-z^4 a^4-2 z^2 a^4+2 a^4+z^7 a^3+3 z^5 a^3+4 z^4 a^2-z^2 a^2+z^3 a }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
