K13a102
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a102/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^4-10 t^3+40 t^2-87 t+113-87 t^{-1} +40 t^{-2} -10 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | Data:K13a102/Conway Polynomial |
| Determinant | 389 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-2 z^6 a^{-2} +3 z^6+3 a^4 z^4-7 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +7 z^4-a^6 z^2+5 a^4 z^2-8 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +7 z^2-a^6+3 a^4-3 a^2-2 a^{-2} + a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{12}+2 z^{12}+7 a^3 z^{11}+17 a z^{11}+10 z^{11} a^{-1} +10 a^4 z^{10}+29 a^2 z^{10}+20 z^{10} a^{-2} +39 z^{10}+8 a^5 z^9+10 a^3 z^9+5 a z^9+24 z^9 a^{-1} +21 z^9 a^{-3} +4 a^6 z^8-14 a^4 z^8-69 a^2 z^8-23 z^8 a^{-2} +13 z^8 a^{-4} -87 z^8+a^7 z^7-18 a^5 z^7-55 a^3 z^7-90 a z^7-98 z^7 a^{-1} -39 z^7 a^{-3} +5 z^7 a^{-5} -11 a^6 z^6-5 a^4 z^6+43 a^2 z^6-9 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} +50 z^6-3 a^7 z^5+13 a^5 z^5+61 a^3 z^5+111 a z^5+103 z^5 a^{-1} +31 z^5 a^{-3} -6 z^5 a^{-5} +11 a^6 z^4+17 a^4 z^4+a^2 z^4+24 z^4 a^{-2} +13 z^4 a^{-4} -z^4 a^{-6} +5 z^4+3 a^7 z^3-3 a^5 z^3-29 a^3 z^3-53 a z^3-45 z^3 a^{-1} -14 z^3 a^{-3} +z^3 a^{-5} -5 a^6 z^2-11 a^4 z^2-11 a^2 z^2-12 z^2 a^{-2} -5 z^2 a^{-4} -12 z^2-a^7 z+5 a^3 z+8 a z+7 z a^{-1} +3 z a^{-3} +a^6+3 a^4+3 a^2+2 a^{-2} + a^{-4} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
