K12a956
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-9 q^{-1} +17 q^{-2} -24 q^{-3} +31 q^{-4} -33 q^{-5} +31 q^{-6} -26 q^{-7} +18 q^{-8} -10 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+26 t^2-42 t+49-42 t^{-1} +26 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+6 z^4+4 z^2+1 }[/math] |
| Determinant | 209 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-3 z^2 a^8-a^8+z^8 a^6+4 z^6 a^6+6 z^4 a^6+4 z^2 a^6+z^8 a^4+4 z^6 a^4+6 z^4 a^4+5 z^2 a^4+2 a^4-z^6 a^2-3 z^4 a^2-2 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+9 z^7 a^{11}-12 z^5 a^{11}+7 z^3 a^{11}-2 z a^{11}+13 z^8 a^{10}-19 z^6 a^{10}+11 z^4 a^{10}-2 z^2 a^{10}+13 z^9 a^9-17 z^7 a^9+4 z^5 a^9+4 z^3 a^9-z a^9+9 z^{10} a^8-7 z^8 a^8-4 z^6 a^8+4 z^2 a^8-a^8+3 z^{11} a^7+13 z^9 a^7-40 z^7 a^7+34 z^5 a^7-13 z^3 a^7+z a^7+16 z^{10} a^6-40 z^8 a^6+39 z^6 a^6-25 z^4 a^6+7 z^2 a^6+3 z^{11} a^5+7 z^9 a^5-36 z^7 a^5+38 z^5 a^5-16 z^3 a^5+z a^5+7 z^{10} a^4-16 z^8 a^4+7 z^6 a^4+2 z^4 a^4-3 z^2 a^4+2 a^4+7 z^9 a^3-21 z^7 a^3+18 z^5 a^3-5 z^3 a^3+z a^3+4 z^8 a^2-13 z^6 a^2+12 z^4 a^2-3 z^2 a^2+z^7 a-3 z^5 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. |
