K13a1117
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a1117/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+31 t^2-77 t+103-77 t^{-1} +31 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | Data:K13a1117/Conway Polynomial |
| Determinant | 329 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -3 z^6 a^{-2} -z^6 a^{-4} -z^6+2 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +z^4 a^{-6} +3 z^4-a^4 z^2-6 z^2 a^{-2} +3 z^2 a^{-4} +6 z^2-a^2-2 a^{-2} +2 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +9 z^{11} a^{-1} +16 z^{11} a^{-3} +7 z^{11} a^{-5} +32 z^{10} a^{-2} +24 z^{10} a^{-4} +9 z^{10} a^{-6} +17 z^{10}+19 a z^9+15 z^9 a^{-1} -13 z^9 a^{-3} -4 z^9 a^{-5} +5 z^9 a^{-7} +15 a^2 z^8-95 z^8 a^{-2} -91 z^8 a^{-4} -29 z^8 a^{-6} +z^8 a^{-8} -19 z^8+9 a^3 z^7-30 a z^7-86 z^7 a^{-1} -76 z^7 a^{-3} -47 z^7 a^{-5} -18 z^7 a^{-7} +4 a^4 z^6-21 a^2 z^6+69 z^6 a^{-2} +88 z^6 a^{-4} +27 z^6 a^{-6} -3 z^6 a^{-8} -14 z^6+a^5 z^5-10 a^3 z^5+19 a z^5+94 z^5 a^{-1} +117 z^5 a^{-3} +75 z^5 a^{-5} +22 z^5 a^{-7} -4 a^4 z^4+15 a^2 z^4-7 z^4 a^{-2} -26 z^4 a^{-4} -5 z^4 a^{-6} +3 z^4 a^{-8} +30 z^4-a^5 z^3+5 a^3 z^3-3 a z^3-41 z^3 a^{-1} -59 z^3 a^{-3} -36 z^3 a^{-5} -9 z^3 a^{-7} +a^4 z^2-5 a^2 z^2-9 z^2 a^{-2} -z^2 a^{-4} -2 z^2 a^{-6} -z^2 a^{-8} -15 z^2-a^3 z+6 z a^{-1} +10 z a^{-3} +5 z a^{-5} +a^2+2 a^{-2} +2 a^{-4} + a^{-6} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
