K12n684
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ - q^{-1} +4 q^{-2} -6 q^{-3} +10 q^{-4} -12 q^{-5} +13 q^{-6} -12 q^{-7} +9 q^{-8} -6 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+10 t^2-15 t+17-15 t^{-1} +10 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+6 z^4+5 z^2+1 }[/math] |
| Determinant | 77 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-5 z^2 a^8-2 a^8+z^8 a^6+6 z^6 a^6+13 z^4 a^6+11 z^2 a^6+2 a^6-z^6 a^4-3 z^4 a^4-z^2 a^4+a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-6 z^4 a^{12}+2 z^2 a^{12}+4 z^7 a^{11}-6 z^5 a^{11}+4 z^8 a^{10}-6 z^6 a^{10}+3 z^4 a^{10}-2 z^2 a^{10}+3 z^9 a^9-5 z^7 a^9+6 z^5 a^9-3 z^3 a^9+z a^9+z^{10} a^8+2 z^8 a^8-6 z^6 a^8+6 z^4 a^8+3 z^2 a^8-2 a^8+4 z^9 a^7-10 z^7 a^7+13 z^5 a^7-5 z^3 a^7+z a^7+z^{10} a^6-2 z^8 a^6+7 z^6 a^6-12 z^4 a^6+9 z^2 a^6-2 a^6+z^9 a^5-z^7 a^5+z^5 a^5-2 z^3 a^5-z a^5+4 z^6 a^4-9 z^4 a^4+2 z^2 a^4+a^4+z^5 a^3-2 z^3 a^3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
