K13a1066
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a1066/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^5+6 t^4-20 t^3+44 t^2-68 t+79-68 t^{-1} +44 t^{-2} -20 t^{-3} +6 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | Data:K13a1066/Conway Polynomial |
| Determinant | 357 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+2 z^8 a^{-2} -7 z^8+5 a^2 z^6+10 z^6 a^{-2} -z^6 a^{-4} -21 z^6+10 a^2 z^4+19 z^4 a^{-2} -3 z^4 a^{-4} -32 z^4+9 a^2 z^2+17 z^2 a^{-2} -3 z^2 a^{-4} -24 z^2+3 a^2+7 a^{-2} -2 a^{-4} -7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12}+10 a z^{11}+21 z^{11} a^{-1} +11 z^{11} a^{-3} +15 a^2 z^{10}+28 z^{10} a^{-2} +16 z^{10} a^{-4} +27 z^{10}+14 a^3 z^9-a z^9-38 z^9 a^{-1} -11 z^9 a^{-3} +12 z^9 a^{-5} +9 a^4 z^8-26 a^2 z^8-107 z^8 a^{-2} -45 z^8 a^{-4} +5 z^8 a^{-6} -92 z^8+4 a^5 z^7-27 a^3 z^7-33 a z^7+z^7 a^{-1} -32 z^7 a^{-3} -34 z^7 a^{-5} +z^7 a^{-7} +a^6 z^6-16 a^4 z^6+23 a^2 z^6+142 z^6 a^{-2} +43 z^6 a^{-4} -12 z^6 a^{-6} +127 z^6-7 a^5 z^5+25 a^3 z^5+52 a z^5+45 z^5 a^{-1} +55 z^5 a^{-3} +28 z^5 a^{-5} -2 z^5 a^{-7} -2 a^6 z^4+10 a^4 z^4-17 a^2 z^4-93 z^4 a^{-2} -22 z^4 a^{-4} +5 z^4 a^{-6} -95 z^4+3 a^5 z^3-15 a^3 z^3-35 a z^3-37 z^3 a^{-1} -29 z^3 a^{-3} -9 z^3 a^{-5} +a^6 z^2-3 a^4 z^2+10 a^2 z^2+33 z^2 a^{-2} +8 z^2 a^{-4} +39 z^2+4 a^3 z+9 a z+9 z a^{-1} +6 z a^{-3} +2 z a^{-5} -3 a^2-7 a^{-2} -2 a^{-4} -7 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
