K12a814
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-3 q^{14}+7 q^{13}-13 q^{12}+18 q^{11}-24 q^{10}+25 q^9-23 q^8+20 q^7-13 q^6+8 q^5-3 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^3-20 t^2+34 t-39+34 t^{-1} -20 t^{-2} +6 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^6+16 z^4+8 z^2+1 }[/math] |
| Determinant | 159 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +3 z^6 a^{-8} +2 z^6 a^{-10} +3 z^4 a^{-6} +11 z^4 a^{-8} +5 z^4 a^{-10} -3 z^4 a^{-12} +2 z^2 a^{-6} +12 z^2 a^{-8} +z^2 a^{-10} -8 z^2 a^{-12} +z^2 a^{-14} +5 a^{-8} -2 a^{-10} -4 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +4 z^{10} a^{-10} +8 z^{10} a^{-12} +4 z^{10} a^{-14} +6 z^9 a^{-9} +12 z^9 a^{-11} +12 z^9 a^{-13} +6 z^9 a^{-15} +6 z^8 a^{-8} -z^8 a^{-10} -15 z^8 a^{-12} -3 z^8 a^{-14} +5 z^8 a^{-16} +3 z^7 a^{-7} -11 z^7 a^{-9} -41 z^7 a^{-11} -45 z^7 a^{-13} -15 z^7 a^{-15} +3 z^7 a^{-17} +z^6 a^{-6} -17 z^6 a^{-8} -14 z^6 a^{-10} +9 z^6 a^{-12} -8 z^6 a^{-14} -12 z^6 a^{-16} +z^6 a^{-18} -7 z^5 a^{-7} +3 z^5 a^{-9} +58 z^5 a^{-11} +74 z^5 a^{-13} +18 z^5 a^{-15} -8 z^5 a^{-17} -3 z^4 a^{-6} +20 z^4 a^{-8} +22 z^4 a^{-10} +3 z^4 a^{-12} +15 z^4 a^{-14} +8 z^4 a^{-16} -3 z^4 a^{-18} +3 z^3 a^{-7} +3 z^3 a^{-9} -37 z^3 a^{-11} -58 z^3 a^{-13} -16 z^3 a^{-15} +5 z^3 a^{-17} +2 z^2 a^{-6} -16 z^2 a^{-8} -14 z^2 a^{-10} +3 z^2 a^{-12} -6 z^2 a^{-14} -3 z^2 a^{-16} +2 z^2 a^{-18} -3 z a^{-9} +10 z a^{-11} +20 z a^{-13} +6 z a^{-15} -z a^{-17} +5 a^{-8} +2 a^{-10} -4 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. |
