K13a309
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a309/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 3 t^4-16 t^3+42 t^2-69 t+81-69 t^{-1} +42 t^{-2} -16 t^{-3} +3 t^{-4} }[/math] |
| Conway polynomial | Data:K13a309/Conway Polynomial |
| Determinant | 341 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^8 a^{-2} +z^8-a^2 z^6+9 z^6 a^{-2} -3 z^6 a^{-4} +3 z^6-3 a^2 z^4+15 z^4 a^{-2} -10 z^4 a^{-4} +z^4 a^{-6} +3 z^4-3 a^2 z^2+11 z^2 a^{-2} -9 z^2 a^{-4} +2 z^2 a^{-6} +2 z^2-a^2+3 a^{-2} -2 a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +10 z^{11} a^{-1} +17 z^{11} a^{-3} +7 z^{11} a^{-5} +37 z^{10} a^{-2} +26 z^{10} a^{-4} +9 z^{10} a^{-6} +20 z^{10}+23 a z^9+17 z^9 a^{-1} -14 z^9 a^{-3} -3 z^9 a^{-5} +5 z^9 a^{-7} +18 a^2 z^8-117 z^8 a^{-2} -102 z^8 a^{-4} -29 z^8 a^{-6} +z^8 a^{-8} -27 z^8+10 a^3 z^7-42 a z^7-102 z^7 a^{-1} -85 z^7 a^{-3} -53 z^7 a^{-5} -18 z^7 a^{-7} +4 a^4 z^6-29 a^2 z^6+112 z^6 a^{-2} +113 z^6 a^{-4} +27 z^6 a^{-6} -3 z^6 a^{-8} -4 z^6+a^5 z^5-11 a^3 z^5+35 a z^5+125 z^5 a^{-1} +145 z^5 a^{-3} +89 z^5 a^{-5} +22 z^5 a^{-7} -3 a^4 z^4+25 a^2 z^4-51 z^4 a^{-2} -52 z^4 a^{-4} -6 z^4 a^{-6} +3 z^4 a^{-8} +20 z^4-a^5 z^3+6 a^3 z^3-14 a z^3-69 z^3 a^{-1} -87 z^3 a^{-3} -49 z^3 a^{-5} -10 z^3 a^{-7} -9 a^2 z^2+13 z^2 a^{-2} +14 z^2 a^{-4} -z^2 a^{-8} -9 z^2-a^3 z+3 a z+14 z a^{-1} +19 z a^{-3} +10 z a^{-5} +z a^{-7} +a^2-3 a^{-2} -2 a^{-4} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
