K12n512
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+3 q^{-1} -5 q^{-2} +9 q^{-3} -10 q^{-4} +11 q^{-5} -10 q^{-6} +8 q^{-7} -6 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-7 t^2+15 t-19+15 t^{-1} -7 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+5 z^4+5 z^2+1 }[/math] |
| Determinant | 67 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+3 z^4 a^6+2 z^2 a^6-a^6+z^6 a^4+4 z^4 a^4+7 z^2 a^4+4 a^4-z^4 a^2-2 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+3 z^8 a^{10}-12 z^6 a^{10}+12 z^4 a^{10}-4 z^2 a^{10}+4 z^9 a^9-16 z^7 a^9+17 z^5 a^9-9 z^3 a^9+3 z a^9+2 z^{10} a^8-3 z^8 a^8-11 z^6 a^8+15 z^4 a^8-3 z^2 a^8-a^8+8 z^9 a^7-34 z^7 a^7+44 z^5 a^7-23 z^3 a^7+4 z a^7+2 z^{10} a^6-3 z^8 a^6-10 z^6 a^6+19 z^4 a^6-8 z^2 a^6+a^6+4 z^9 a^5-16 z^7 a^5+22 z^5 a^5-8 z^3 a^5-z a^5+3 z^8 a^4-11 z^6 a^4+19 z^4 a^4-13 z^2 a^4+4 a^4+z^7 a^3-z^5 a^3+3 z^3 a^3-2 z a^3+3 z^4 a^2-4 z^2 a^2+a^2+z^3 a-z a }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
