K12n166
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{14}-3 q^{13}+4 q^{12}-6 q^{11}+6 q^{10}-6 q^9+6 q^8-4 q^7+3 q^6-q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-4 t^3+5 t^2-6 t+7-6 t^{-1} +5 t^{-2} -4 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+12 z^6+21 z^4+10 z^2+1 }[/math] |
| Determinant | 41 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +z^8 a^{-10} +7 z^6 a^{-8} +6 z^6 a^{-10} -z^6 a^{-12} +16 z^4 a^{-8} +11 z^4 a^{-10} -6 z^4 a^{-12} +13 z^2 a^{-8} +7 z^2 a^{-10} -11 z^2 a^{-12} +z^2 a^{-14} +3 a^{-8} +2 a^{-10} -6 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +3 z^9 a^{-11} +2 z^9 a^{-13} +z^8 a^{-8} -5 z^8 a^{-10} -4 z^8 a^{-12} +2 z^8 a^{-14} -5 z^7 a^{-9} -15 z^7 a^{-11} -8 z^7 a^{-13} +2 z^7 a^{-15} -7 z^6 a^{-8} +8 z^6 a^{-10} +10 z^6 a^{-12} -4 z^6 a^{-14} +z^6 a^{-16} +6 z^5 a^{-9} +25 z^5 a^{-11} +15 z^5 a^{-13} -4 z^5 a^{-15} +16 z^4 a^{-8} -7 z^4 a^{-10} -24 z^4 a^{-12} -z^4 a^{-14} +z^3 a^{-9} -20 z^3 a^{-11} -21 z^3 a^{-13} +3 z^3 a^{-15} +3 z^3 a^{-17} -13 z^2 a^{-8} +6 z^2 a^{-10} +22 z^2 a^{-12} +3 z^2 a^{-14} +z^2 a^{-16} +z^2 a^{-18} -2 z a^{-9} +7 z a^{-11} +9 z a^{-13} -z a^{-15} -z a^{-17} +3 a^{-8} -2 a^{-10} -6 a^{-12} -2 a^{-14} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
