K12n308
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-3 q^{12}+5 q^{11}-9 q^{10}+10 q^9-10 q^8+10 q^7-7 q^6+5 q^5-2 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-10 t^2+12 t-11+12 t^{-1} -10 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+14 z^4+8 z^2+1 }[/math] |
| Determinant | 63 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +2 z^6 a^{-8} +z^6 a^{-10} +4 z^4 a^{-6} +8 z^4 a^{-8} +3 z^4 a^{-10} -z^4 a^{-12} +4 z^2 a^{-6} +8 z^2 a^{-8} -4 z^2 a^{-12} + a^{-6} +3 a^{-8} -2 a^{-10} -2 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +2 z^9 a^{-9} +4 z^9 a^{-11} +2 z^9 a^{-13} +3 z^8 a^{-8} -2 z^8 a^{-12} +z^8 a^{-14} +2 z^7 a^{-7} -3 z^7 a^{-9} -14 z^7 a^{-11} -9 z^7 a^{-13} +z^6 a^{-6} -10 z^6 a^{-8} -6 z^6 a^{-10} +3 z^6 a^{-12} -2 z^6 a^{-14} -6 z^5 a^{-7} -5 z^5 a^{-9} +21 z^5 a^{-11} +23 z^5 a^{-13} +3 z^5 a^{-15} -4 z^4 a^{-6} +11 z^4 a^{-8} +11 z^4 a^{-10} +5 z^4 a^{-14} +z^4 a^{-16} +3 z^3 a^{-7} +9 z^3 a^{-9} -10 z^3 a^{-11} -22 z^3 a^{-13} -6 z^3 a^{-15} +4 z^2 a^{-6} -9 z^2 a^{-8} -9 z^2 a^{-10} +3 z^2 a^{-12} -3 z^2 a^{-14} -2 z^2 a^{-16} -5 z a^{-9} +z a^{-11} +9 z a^{-13} +3 z a^{-15} - a^{-6} +3 a^{-8} +2 a^{-10} -2 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. |
