K12a1267
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-12 q^3+17 q^2-21 q+23-21 q^{-1} +17 q^{-2} -12 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-32 t+41-32 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-8 z^4-4 z^2+1 }[/math] |
| Determinant | 145 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-2 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} -6 z^4+2 a^4 z^2-a^2 z^2-z^2 a^{-2} +2 z^2 a^{-4} -6 z^2+a^4+ a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+5 z^{10} a^{-2} +10 z^{10}+6 a^3 z^9+3 a z^9+3 z^9 a^{-1} +6 z^9 a^{-3} +5 a^4 z^8-13 a^2 z^8-13 z^8 a^{-2} +5 z^8 a^{-4} -36 z^8+3 a^5 z^7-17 a^3 z^7-26 a z^7-26 z^7 a^{-1} -17 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-13 a^4 z^6+14 a^2 z^6+14 z^6 a^{-2} -13 z^6 a^{-4} +z^6 a^{-6} +56 z^6-8 a^5 z^5+20 a^3 z^5+51 a z^5+51 z^5 a^{-1} +20 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+9 a^4 z^4-5 a^2 z^4-5 z^4 a^{-2} +9 z^4 a^{-4} -3 z^4 a^{-6} -34 z^4+4 a^5 z^3-16 a^3 z^3-34 a z^3-34 z^3 a^{-1} -16 z^3 a^{-3} +4 z^3 a^{-5} +2 a^6 z^2-5 a^4 z^2-a^2 z^2-z^2 a^{-2} -5 z^2 a^{-4} +2 z^2 a^{-6} +12 z^2+4 a^3 z+8 a z+8 z a^{-1} +4 z a^{-3} +a^4+ a^{-4} -1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
