K13a2291
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a2291/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+23 t^2-47 t+57-47 t^{-1} +23 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | Data:K13a2291/Conway Polynomial |
| Determinant | 205 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{12}-a^{12}+2 z^4 a^{10}+2 z^2 a^{10}-a^{10}-z^6 a^8+z^4 a^8+6 z^2 a^8+3 a^8-2 z^6 a^6-4 z^4 a^6-2 z^2 a^6-a^6-z^6 a^4-z^4 a^4+2 z^2 a^4+a^4+z^4 a^2+2 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{15}-4 z^5 a^{15}+5 z^3 a^{15}-2 z a^{15}+3 z^8 a^{14}-10 z^6 a^{14}+9 z^4 a^{14}-2 z^2 a^{14}+5 z^9 a^{13}-15 z^7 a^{13}+13 z^5 a^{13}-7 z^3 a^{13}+3 z a^{13}+5 z^{10} a^{12}-11 z^8 a^{12}+4 z^6 a^{12}-2 z^4 a^{12}+2 z^2 a^{12}-a^{12}+3 z^{11} a^{11}-15 z^7 a^{11}+17 z^5 a^{11}-10 z^3 a^{11}+2 z a^{11}+z^{12} a^{10}+6 z^{10} a^{10}-16 z^8 a^{10}+9 z^6 a^{10}+3 z^4 a^{10}-5 z^2 a^{10}+a^{10}+6 z^{11} a^9-11 z^9 a^9+11 z^7 a^9-11 z^5 a^9+11 z^3 a^9-3 z a^9+z^{12} a^8+6 z^{10} a^8-15 z^8 a^8+15 z^6 a^8-z^4 a^8-4 z^2 a^8+3 a^8+3 z^{11} a^7-7 z^7 a^7+13 z^5 a^7-7 z^3 a^7+z a^7+5 z^{10} a^6-8 z^8 a^6+7 z^6 a^6-3 z^4 a^6-z^2 a^6+a^6+6 z^9 a^5-14 z^7 a^5+16 z^5 a^5-11 z^3 a^5+z a^5+5 z^8 a^4-12 z^6 a^4+9 z^4 a^4-4 z^2 a^4+a^4+3 z^7 a^3-8 z^5 a^3+5 z^3 a^3+z^6 a^2-3 z^4 a^2+2 z^2 a^2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
