K13n3223
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n3223/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+12 t^2-30 t+41-30 t^{-1} +12 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | Data:K13n3223/Conway Polynomial |
| Determinant | 129 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6+a^4 z^4-3 a^2 z^4+3 z^4 a^{-2} -z^4+2 a^4 z^2-5 a^2 z^2+5 z^2 a^{-2} -2 z^2 a^{-4} +a^4-2 a^2+2 a^{-2} - a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +4 a^2 z^{10}+5 z^{10} a^{-2} +9 z^{10}+4 a^3 z^9-a z^9-z^9 a^{-1} +4 z^9 a^{-3} +4 a^4 z^8-10 a^2 z^8-21 z^8 a^{-2} +z^8 a^{-4} -36 z^8+3 a^5 z^7-6 a^3 z^7-8 a z^7-11 z^7 a^{-1} -12 z^7 a^{-3} +a^6 z^6-9 a^4 z^6+11 a^2 z^6+45 z^6 a^{-2} +4 z^6 a^{-4} +62 z^6-9 a^5 z^5-5 a^3 z^5+17 a z^5+27 z^5 a^{-1} +17 z^5 a^{-3} +3 z^5 a^{-5} -3 a^6 z^4+3 a^4 z^4-3 a^2 z^4-46 z^4 a^{-2} -16 z^4 a^{-4} -39 z^4+7 a^5 z^3+9 a^3 z^3-4 a z^3-14 z^3 a^{-1} -15 z^3 a^{-3} -7 z^3 a^{-5} +2 a^6 z^2-a^4 z^2-5 a^2 z^2+19 z^2 a^{-2} +9 z^2 a^{-4} +8 z^2-2 a^5 z-4 a^3 z-2 a z+2 z a^{-1} +4 z a^{-3} +2 z a^{-5} +a^4+2 a^2-2 a^{-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. |
