K12a1255
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+9 q^8-15 q^7+21 q^6-26 q^5+27 q^4-25 q^3+21 q^2-14 q+9-4 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-13 t^3+23 t^2-30 t+33-30 t^{-1} +23 t^{-2} -13 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-5 z^8-8 z^6-5 z^4+1 }[/math] |
| Determinant | 177 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -7 z^8 a^{-4} +z^8 a^{-6} +5 z^6 a^{-2} -18 z^6 a^{-4} +5 z^6 a^{-6} +8 z^4 a^{-2} -21 z^4 a^{-4} +8 z^4 a^{-6} +6 z^2 a^{-2} -11 z^2 a^{-4} +5 z^2 a^{-6} +3 a^{-2} -3 a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +6 z^{10} a^{-2} +15 z^{10} a^{-4} +9 z^{10} a^{-6} +4 z^9 a^{-1} +10 z^9 a^{-5} +14 z^9 a^{-7} -24 z^8 a^{-2} -52 z^8 a^{-4} -11 z^8 a^{-6} +16 z^8 a^{-8} +z^8-17 z^7 a^{-1} -33 z^7 a^{-3} -53 z^7 a^{-5} -23 z^7 a^{-7} +14 z^7 a^{-9} +28 z^6 a^{-2} +53 z^6 a^{-4} -13 z^6 a^{-6} -25 z^6 a^{-8} +9 z^6 a^{-10} -4 z^6+22 z^5 a^{-1} +51 z^5 a^{-3} +54 z^5 a^{-5} +3 z^5 a^{-7} -18 z^5 a^{-9} +4 z^5 a^{-11} -10 z^4 a^{-2} -23 z^4 a^{-4} +9 z^4 a^{-6} +9 z^4 a^{-8} -7 z^4 a^{-10} +z^4 a^{-12} +5 z^4-9 z^3 a^{-1} -22 z^3 a^{-3} -21 z^3 a^{-5} +z^3 a^{-7} +8 z^3 a^{-9} -z^3 a^{-11} +4 z^2 a^{-2} +10 z^2 a^{-4} +z^2 a^{-6} -z^2 a^{-8} +2 z^2 a^{-10} -2 z^2+z a^{-1} +4 z a^{-3} +4 z a^{-5} -z a^{-9} -3 a^{-2} -3 a^{-4} - a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
