K12n587
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+14 q^2-18 q+20-18 q^{-1} +16 q^{-2} -10 q^{-3} +5 q^{-4} -2 q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+10 t^2-28 t+39-28 t^{-1} +10 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+4 z^4+3 z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6+3 a^2 z^4+2 z^4 a^{-2} -z^4-2 a^4 z^2+5 a^2 z^2+z^2 a^{-2} -z^2 a^{-4} -2 a^4+3 a^2- a^{-2} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+2 a^3 z^9+7 a z^9+5 z^9 a^{-1} +a^4 z^8+6 a^2 z^8+9 z^8 a^{-2} +14 z^8-a^3 z^7-6 a z^7+3 z^7 a^{-1} +8 z^7 a^{-3} +2 a^4 z^6-12 a^2 z^6-14 z^6 a^{-2} +4 z^6 a^{-4} -32 z^6+3 a^5 z^5+4 a^3 z^5-4 a z^5-19 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} -6 a^4 z^4+7 a^2 z^4+8 z^4 a^{-2} -5 z^4 a^{-4} +26 z^4-7 a^5 z^3-11 a^3 z^3+3 a z^3+15 z^3 a^{-1} +7 z^3 a^{-3} -z^3 a^{-5} +4 a^4 z^2-4 z^2 a^{-2} +z^2 a^{-4} -9 z^2+4 a^5 z+6 a^3 z+a z-3 z a^{-1} -2 z a^{-3} -2 a^4-3 a^2+ a^{-2} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
