K12a502
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-3 q^{12}+5 q^{11}-8 q^{10}+11 q^9-13 q^8+13 q^7-12 q^6+10 q^5-7 q^4+5 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-13 t^2+15 t-15+15 t^{-1} -13 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-5 z^4+3 z^2+1 }[/math] |
| Determinant | 91 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -7 z^4 a^{-6} -7 z^4 a^{-8} +4 z^4 a^{-10} +7 z^2 a^{-4} -4 z^2 a^{-6} -3 z^2 a^{-8} +3 z^2 a^{-10} +3 a^{-4} -2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +5 z^{10} a^{-8} +3 z^{10} a^{-10} +2 z^9 a^{-5} +2 z^9 a^{-9} +4 z^9 a^{-11} +z^8 a^{-4} -7 z^8 a^{-6} -20 z^8 a^{-8} -8 z^8 a^{-10} +4 z^8 a^{-12} -10 z^7 a^{-5} -14 z^7 a^{-7} -17 z^7 a^{-9} -9 z^7 a^{-11} +4 z^7 a^{-13} -6 z^6 a^{-4} +22 z^6 a^{-8} +8 z^6 a^{-10} -4 z^6 a^{-12} +4 z^6 a^{-14} +14 z^5 a^{-5} +21 z^5 a^{-7} +21 z^5 a^{-9} +9 z^5 a^{-11} -2 z^5 a^{-13} +3 z^5 a^{-15} +12 z^4 a^{-4} +14 z^4 a^{-6} -9 z^4 a^{-8} -7 z^4 a^{-10} -z^4 a^{-12} -4 z^4 a^{-14} +z^4 a^{-16} -5 z^3 a^{-5} -8 z^3 a^{-7} -10 z^3 a^{-9} -6 z^3 a^{-11} -3 z^3 a^{-13} -4 z^3 a^{-15} -10 z^2 a^{-4} -10 z^2 a^{-6} +2 z^2 a^{-8} +2 z^2 a^{-10} +2 z^2 a^{-12} +z^2 a^{-14} -z^2 a^{-16} -z a^{-5} +z a^{-7} +2 z a^{-9} +z a^{-11} +2 z a^{-13} +z a^{-15} +3 a^{-4} +2 a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
