K12a367
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{16}-4 q^{15}+8 q^{14}-13 q^{13}+17 q^{12}-20 q^{11}+20 q^{10}-18 q^9+14 q^8-9 q^7+6 q^6-2 q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^4-9 t^3+17 t^2-24 t+27-24 t^{-1} +17 t^{-2} -9 t^{-3} +3 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^8+15 z^6+23 z^4+11 z^2+1 }[/math] |
| Determinant | 133 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +2 z^8 a^{-10} +6 z^6 a^{-8} +12 z^6 a^{-10} -3 z^6 a^{-12} +12 z^4 a^{-8} +24 z^4 a^{-10} -14 z^4 a^{-12} +z^4 a^{-14} +9 z^2 a^{-8} +18 z^2 a^{-10} -19 z^2 a^{-12} +3 z^2 a^{-14} +2 a^{-8} +4 a^{-10} -7 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +3 z^{10} a^{-10} +7 z^{10} a^{-12} +4 z^{10} a^{-14} +2 z^9 a^{-9} +4 z^9 a^{-11} +10 z^9 a^{-13} +8 z^9 a^{-15} +z^8 a^{-8} -14 z^8 a^{-10} -24 z^8 a^{-12} +2 z^8 a^{-14} +11 z^8 a^{-16} -9 z^7 a^{-9} -31 z^7 a^{-11} -42 z^7 a^{-13} -9 z^7 a^{-15} +11 z^7 a^{-17} -6 z^6 a^{-8} +24 z^6 a^{-10} +29 z^6 a^{-12} -25 z^6 a^{-14} -16 z^6 a^{-16} +8 z^6 a^{-18} +11 z^5 a^{-9} +52 z^5 a^{-11} +52 z^5 a^{-13} -7 z^5 a^{-15} -14 z^5 a^{-17} +4 z^5 a^{-19} +12 z^4 a^{-8} -24 z^4 a^{-10} -29 z^4 a^{-12} +20 z^4 a^{-14} +5 z^4 a^{-16} -7 z^4 a^{-18} +z^4 a^{-20} -2 z^3 a^{-9} -34 z^3 a^{-11} -32 z^3 a^{-13} +7 z^3 a^{-15} +5 z^3 a^{-17} -2 z^3 a^{-19} -9 z^2 a^{-8} +16 z^2 a^{-10} +24 z^2 a^{-12} -2 z^2 a^{-14} +z^2 a^{-18} -z a^{-9} +8 z a^{-11} +8 z a^{-13} -z a^{-15} +2 a^{-8} -4 a^{-10} -7 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. |
