K12n104
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-5 q^{-1} +8 q^{-2} -10 q^{-3} +12 q^{-4} -11 q^{-5} +10 q^{-6} -7 q^{-7} +4 q^{-8} -2 q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+10 t^2-14 t+15-14 t^{-1} +10 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+6 z^4+6 z^2+1 }[/math] |
| Determinant | 73 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^8-2 a^8-z^6 a^6-3 z^4 a^6-z^2 a^6+a^6+z^8 a^4+6 z^6 a^4+13 z^4 a^4+12 z^2 a^4+3 a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^3 a^{11}-3 z a^{11}+z^6 a^{10}+2 z^4 a^{10}-z^2 a^{10}+2 z^7 a^9+z^3 a^9+2 z^8 a^8+2 z^6 a^8-8 z^4 a^8+8 z^2 a^8-2 a^8+2 z^9 a^7-z^7 a^7-5 z^3 a^7+3 z a^7+z^{10} a^6+2 z^8 a^6-8 z^6 a^6+3 z^4 a^6-a^6+5 z^9 a^5-14 z^7 a^5+9 z^5 a^5-2 z^3 a^5-z a^5+z^{10} a^4+3 z^8 a^4-22 z^6 a^4+29 z^4 a^4-15 z^2 a^4+3 a^4+3 z^9 a^3-10 z^7 a^3+5 z^5 a^3+5 z^3 a^3-2 z a^3+3 z^8 a^2-13 z^6 a^2+16 z^4 a^2-6 z^2 a^2+a^2+z^7 a-4 z^5 a+4 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. |
