K12a1285
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+5 q^3-8 q^2+10 q-12+13 q^{-1} -12 q^{-2} +10 q^{-3} -7 q^{-4} +4 q^{-5} -2 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+6 t^3-11 t^2+16 t-17+16 t^{-1} -11 t^{-2} +6 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-10 z^6-15 z^4-6 z^2+1 }[/math] |
| Determinant | 87 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-6 a^2 z^6+z^6 a^{-2} -6 z^6+5 a^4 z^4-12 a^2 z^4+5 z^4 a^{-2} -13 z^4+7 a^4 z^2-8 a^2 z^2+8 z^2 a^{-2} -13 z^2+2 a^4+4 a^{-2} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+2 z^{10} a^{-2} +5 z^{10}+5 a^3 z^9+2 a z^9-z^9 a^{-1} +2 z^9 a^{-3} +5 a^4 z^8-8 a^2 z^8-8 z^8 a^{-2} +z^8 a^{-4} -22 z^8+4 a^5 z^7-19 a^3 z^7-19 a z^7-6 z^7 a^{-1} -10 z^7 a^{-3} +3 a^6 z^6-16 a^4 z^6+3 a^2 z^6+9 z^6 a^{-2} -6 z^6 a^{-4} +37 z^6+2 a^7 z^5-9 a^5 z^5+31 a^3 z^5+30 a z^5+3 z^5 a^{-1} +15 z^5 a^{-3} +a^8 z^4-5 a^6 z^4+23 a^4 z^4+7 a^2 z^4-9 z^4 a^{-2} +12 z^4 a^{-4} -43 z^4-3 a^7 z^3+9 a^5 z^3-22 a^3 z^3-23 a z^3+4 z^3 a^{-1} -7 z^3 a^{-3} -2 a^8 z^2+3 a^6 z^2-11 a^4 z^2-9 a^2 z^2+12 z^2 a^{-2} -8 z^2 a^{-4} +27 z^2+5 a^3 z+5 a z+z a^{-1} +z a^{-3} +2 a^4-4 a^{-2} -5 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
