K13a3720
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a3720/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-31 t^2+54 t-63+54 t^{-1} -31 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a3720/Conway Polynomial |
| Determinant | 259 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8+2 a^2 z^6-4 z^6 a^{-2} +z^6 a^{-4} -4 z^6-a^4 z^4+7 a^2 z^4-6 z^4 a^{-2} +3 z^4 a^{-4} -8 z^4-2 a^4 z^2+9 a^2 z^2-3 z^2 a^{-2} +3 z^2 a^{-4} -10 z^2-a^4+5 a^2+ a^{-2} + a^{-4} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{12}+2 z^{12}+5 a^3 z^{11}+14 a z^{11}+9 z^{11} a^{-1} +4 a^4 z^{10}+9 a^2 z^{10}+19 z^{10} a^{-2} +24 z^{10}+a^5 z^9-19 a^3 z^9-42 a z^9+4 z^9 a^{-1} +26 z^9 a^{-3} -21 a^4 z^8-74 a^2 z^8-34 z^8 a^{-2} +25 z^8 a^{-4} -112 z^8-5 a^5 z^7+12 a^3 z^7+4 a z^7-88 z^7 a^{-1} -57 z^7 a^{-3} +18 z^7 a^{-5} +39 a^4 z^6+138 a^2 z^6-11 z^6 a^{-2} -46 z^6 a^{-4} +10 z^6 a^{-6} +144 z^6+9 a^5 z^5+25 a^3 z^5+69 a z^5+115 z^5 a^{-1} +36 z^5 a^{-3} -22 z^5 a^{-5} +4 z^5 a^{-7} -30 a^4 z^4-100 a^2 z^4+23 z^4 a^{-2} +26 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} -80 z^4-7 a^5 z^3-29 a^3 z^3-51 a z^3-55 z^3 a^{-1} -18 z^3 a^{-3} +8 z^3 a^{-5} +9 a^4 z^2+33 a^2 z^2-5 z^2 a^{-2} -8 z^2 a^{-4} +2 z^2 a^{-6} +29 z^2+2 a^5 z+7 a^3 z+10 a z+10 z a^{-1} +5 z a^{-3} -a^4-5 a^2- a^{-2} + a^{-4} -5 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
