K12n251
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{12}+q^{11}-2 q^{10}+3 q^9-3 q^8+3 q^7-2 q^6+2 q^5-q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-5 t^2+2 t+1+2 t^{-1} -5 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+13 z^4+9 z^2+1 }[/math] |
| Determinant | 19 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-6} +4 z^4 a^{-8} +5 z^4 a^{-10} -z^4 a^{-12} +6 z^2 a^{-6} +2 z^2 a^{-8} +6 z^2 a^{-10} -5 z^2 a^{-12} +2 a^{-6} - a^{-8} +3 a^{-10} -4 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +2 z^9 a^{-11} +z^9 a^{-13} +z^8 a^{-8} -7 z^8 a^{-10} -8 z^8 a^{-12} +z^7 a^{-7} -5 z^7 a^{-9} -14 z^7 a^{-11} -8 z^7 a^{-13} +z^6 a^{-6} -4 z^6 a^{-8} +18 z^6 a^{-10} +23 z^6 a^{-12} -4 z^5 a^{-7} +7 z^5 a^{-9} +33 z^5 a^{-11} +22 z^5 a^{-13} -5 z^4 a^{-6} +2 z^4 a^{-8} -22 z^4 a^{-10} -29 z^4 a^{-12} +2 z^3 a^{-7} -4 z^3 a^{-9} -29 z^3 a^{-11} -23 z^3 a^{-13} +6 z^2 a^{-6} +2 z^2 a^{-8} +13 z^2 a^{-10} +18 z^2 a^{-12} +z^2 a^{-14} +z a^{-7} +z a^{-9} +8 z a^{-11} +8 z a^{-13} -2 a^{-6} - a^{-8} -3 a^{-10} -4 a^{-12} - a^{-14} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
