K12a393
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-5 q^{11}+13 q^{10}-23 q^9+32 q^8-40 q^7+42 q^6-38 q^5+31 q^4-20 q^3+11 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+27 t^2-60 t+77-60 t^{-1} +27 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-3 z^4+3 z^2+1 }[/math] |
| Determinant | 261 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} +z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +z^4 a^{-10} +z^2 a^{-2} +5 z^2 a^{-4} -6 z^2 a^{-6} +3 z^2 a^{-8} +3 a^{-4} -2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-7} +3 z^{11} a^{-9} +9 z^{10} a^{-6} +20 z^{10} a^{-8} +11 z^{10} a^{-10} +12 z^9 a^{-5} +24 z^9 a^{-7} +28 z^9 a^{-9} +16 z^9 a^{-11} +9 z^8 a^{-4} -24 z^8 a^{-8} -3 z^8 a^{-10} +12 z^8 a^{-12} +4 z^7 a^{-3} -21 z^7 a^{-5} -65 z^7 a^{-7} -75 z^7 a^{-9} -30 z^7 a^{-11} +5 z^7 a^{-13} +z^6 a^{-2} -18 z^6 a^{-4} -30 z^6 a^{-6} -15 z^6 a^{-8} -27 z^6 a^{-10} -22 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +15 z^5 a^{-5} +59 z^5 a^{-7} +63 z^5 a^{-9} +19 z^5 a^{-11} -7 z^5 a^{-13} -2 z^4 a^{-2} +16 z^4 a^{-4} +38 z^4 a^{-6} +30 z^4 a^{-8} +23 z^4 a^{-10} +12 z^4 a^{-12} -z^4 a^{-14} +3 z^3 a^{-3} -6 z^3 a^{-5} -24 z^3 a^{-7} -25 z^3 a^{-9} -8 z^3 a^{-11} +2 z^3 a^{-13} +z^2 a^{-2} -10 z^2 a^{-4} -18 z^2 a^{-6} -10 z^2 a^{-8} -6 z^2 a^{-10} -3 z^2 a^{-12} +5 z a^{-7} +7 z a^{-9} +2 z a^{-11} +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. |
