K13a11
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a11/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^4-10 t^3+42 t^2-95 t+125-95 t^{-1} +42 t^{-2} -10 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | Data:K13a11/Conway Polynomial |
| Determinant | 421 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-2 z^6 a^{-2} +3 z^6+3 a^4 z^4-6 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +8 z^4-a^6 z^2+3 a^4 z^2-7 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} +9 z^2+a^4-3 a^2-3 a^{-2} + a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{12}+2 z^{12}+8 a^3 z^{11}+18 a z^{11}+10 z^{11} a^{-1} +13 a^4 z^{10}+37 a^2 z^{10}+20 z^{10} a^{-2} +44 z^{10}+11 a^5 z^9+20 a^3 z^9+21 a z^9+33 z^9 a^{-1} +21 z^9 a^{-3} +5 a^6 z^8-17 a^4 z^8-78 a^2 z^8-15 z^8 a^{-2} +13 z^8 a^{-4} -84 z^8+a^7 z^7-26 a^5 z^7-90 a^3 z^7-138 a z^7-115 z^7 a^{-1} -35 z^7 a^{-3} +5 z^7 a^{-5} -12 a^6 z^6-11 a^4 z^6+23 a^2 z^6-24 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} +19 z^6-2 a^7 z^5+23 a^5 z^5+96 a^3 z^5+152 a z^5+114 z^5 a^{-1} +27 z^5 a^{-3} -6 z^5 a^{-5} +10 a^6 z^4+25 a^4 z^4+30 a^2 z^4+36 z^4 a^{-2} +14 z^4 a^{-4} -z^4 a^{-6} +36 z^4+a^7 z^3-9 a^5 z^3-40 a^3 z^3-68 a z^3-52 z^3 a^{-1} -12 z^3 a^{-3} +2 z^3 a^{-5} -3 a^6 z^2-10 a^4 z^2-19 a^2 z^2-18 z^2 a^{-2} -5 z^2 a^{-4} -25 z^2+a^5 z+6 a^3 z+11 a z+9 z a^{-1} +3 z a^{-3} +a^4+3 a^2+3 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. |
