K12n693
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+4 q^{10}-5 q^9+4 q^8-3 q^7+2 q^6+q^5-2 q^4+3 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-2 t^2-7 t+13-7 t^{-1} -2 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6+2 z^4+5 z^2+1 }[/math] |
| Determinant | 13 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} +z^6 a^{-4} -6 z^6 a^{-6} +z^6 a^{-8} +5 z^4 a^{-4} -10 z^4 a^{-6} +7 z^4 a^{-8} +6 z^2 a^{-4} -7 z^2 a^{-6} +10 z^2 a^{-8} -4 z^2 a^{-10} +2 a^{-4} -2 a^{-6} +4 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +3 z^9 a^{-7} +2 z^9 a^{-9} +z^9 a^{-11} +z^8 a^{-4} -4 z^8 a^{-6} -5 z^8 a^{-8} +3 z^8 a^{-10} +3 z^8 a^{-12} -12 z^7 a^{-5} -21 z^7 a^{-7} -13 z^7 a^{-9} -z^7 a^{-11} +3 z^7 a^{-13} -6 z^6 a^{-4} -4 z^6 a^{-6} -3 z^6 a^{-8} -17 z^6 a^{-10} -11 z^6 a^{-12} +z^6 a^{-14} +20 z^5 a^{-5} +38 z^5 a^{-7} +18 z^5 a^{-9} -11 z^5 a^{-11} -11 z^5 a^{-13} +11 z^4 a^{-4} +19 z^4 a^{-6} +23 z^4 a^{-8} +25 z^4 a^{-10} +7 z^4 a^{-12} -3 z^4 a^{-14} -11 z^3 a^{-5} -22 z^3 a^{-7} -3 z^3 a^{-9} +16 z^3 a^{-11} +8 z^3 a^{-13} -8 z^2 a^{-4} -13 z^2 a^{-6} -17 z^2 a^{-8} -15 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +z a^{-5} +4 z a^{-7} -2 z a^{-9} -7 z a^{-11} -2 z a^{-13} +2 a^{-4} +2 a^{-6} +4 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
