K12a861
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-8 q^{-1} +16 q^{-2} -23 q^{-3} +29 q^{-4} -32 q^{-5} +30 q^{-6} -25 q^{-7} +18 q^{-8} -10 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+25 t^2-40 t+47-40 t^{-1} +25 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+5 z^4+2 z^2+1 }[/math] |
| Determinant | 201 |
| 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+5 z^2 a^6+2 a^6+z^8 a^4+4 z^6 a^4+5 z^4 a^4+z^2 a^4-2 a^4-z^6 a^2-3 z^4 a^2-z^2 a^2+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}-z a^{11}+13 z^8 a^{10}-20 z^6 a^{10}+14 z^4 a^{10}-3 z^2 a^{10}+12 z^9 a^9-14 z^7 a^9+4 z^5 a^9+z a^9+7 z^{10} a^8+2 z^8 a^8-16 z^6 a^8+6 z^4 a^8+z^2 a^8-a^8+2 z^{11} a^7+15 z^9 a^7-35 z^7 a^7+25 z^5 a^7-16 z^3 a^7+5 z a^7+12 z^{10} a^6-21 z^8 a^6+12 z^6 a^6-14 z^4 a^6+8 z^2 a^6-2 a^6+2 z^{11} a^5+9 z^9 a^5-30 z^7 a^5+24 z^5 a^5-12 z^3 a^5+5 z a^5+5 z^{10} a^4-6 z^8 a^4-10 z^6 a^4+13 z^4 a^4-2 a^4+6 z^9 a^3-17 z^7 a^3+13 z^5 a^3-2 z^3 a^3+2 z a^3+4 z^8 a^2-14 z^6 a^2+15 z^4 a^2-3 z^2 a^2-2 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. |
