K13a3027
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a3027/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+38 t^2-88 t+117-88 t^{-1} +38 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | Data:K13a3027/Conway Polynomial |
| Determinant | 389 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-4 z^2 a^6-3 a^6+6 z^4 a^4+9 z^2 a^4+4 a^4-4 z^6 a^2-10 z^4 a^2-11 z^2 a^2-3 a^2+z^8+4 z^6+10 z^4+8 z^2+2-z^6 a^{-2} -2 z^4 a^{-2} -3 z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^4 z^{12}+3 a^2 z^{12}+7 a^5 z^{11}+21 a^3 z^{11}+14 a z^{11}+7 a^6 z^{10}+19 a^4 z^{10}+41 a^2 z^{10}+29 z^{10}+4 a^7 z^9-6 a^5 z^9-25 a^3 z^9+20 a z^9+35 z^9 a^{-1} +a^8 z^8-19 a^6 z^8-70 a^4 z^8-111 a^2 z^8+27 z^8 a^{-2} -34 z^8-15 a^7 z^7-33 a^5 z^7-56 a^3 z^7-111 a z^7-59 z^7 a^{-1} +14 z^7 a^{-3} -4 a^8 z^6+10 a^6 z^6+52 a^4 z^6+60 a^2 z^6-37 z^6 a^{-2} +5 z^6 a^{-4} -20 z^6+21 a^7 z^5+60 a^5 z^5+92 a^3 z^5+100 a z^5+36 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +6 a^8 z^4+12 a^6 z^4+10 a^4 z^4+15 a^2 z^4+22 z^4 a^{-2} -z^4 a^{-4} +34 z^4-13 a^7 z^3-35 a^5 z^3-42 a^3 z^3-34 a z^3-11 z^3 a^{-1} +3 z^3 a^{-3} -4 a^8 z^2-13 a^6 z^2-18 a^4 z^2-17 a^2 z^2-6 z^2 a^{-2} -14 z^2+3 a^7 z+7 a^5 z+7 a^3 z+4 a z+z a^{-1} +a^8+3 a^6+4 a^4+3 a^2+2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
