K13a3480
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a3480/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+14 t^3-47 t^2+92 t-113+92 t^{-1} -47 t^{-2} +14 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a3480/Conway Polynomial |
| Determinant | 423 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -2 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +2 z^6-a^2 z^4-3 z^4 a^{-2} -5 z^4 a^{-4} +2 z^4 a^{-6} +4 z^4-a^2 z^2-5 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2 a^{-6} +4 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{12} a^{-2} +5 z^{12} a^{-4} +13 z^{11} a^{-1} +30 z^{11} a^{-3} +17 z^{11} a^{-5} +25 z^{10} a^{-2} +35 z^{10} a^{-4} +25 z^{10} a^{-6} +15 z^{10}+11 a z^9-12 z^9 a^{-1} -57 z^9 a^{-3} -12 z^9 a^{-5} +22 z^9 a^{-7} +5 a^2 z^8-87 z^8 a^{-2} -115 z^8 a^{-4} -48 z^8 a^{-6} +13 z^8 a^{-8} -28 z^8+a^3 z^7-25 a z^7-27 z^7 a^{-1} +14 z^7 a^{-3} -31 z^7 a^{-5} -41 z^7 a^{-7} +5 z^7 a^{-9} -12 a^2 z^6+79 z^6 a^{-2} +122 z^6 a^{-4} +37 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} +3 z^6-2 a^3 z^5+16 a z^5+40 z^5 a^{-1} +34 z^5 a^{-3} +47 z^5 a^{-5} +29 z^5 a^{-7} -6 z^5 a^{-9} +9 a^2 z^4-14 z^4 a^{-2} -47 z^4 a^{-4} -15 z^4 a^{-6} +9 z^4 a^{-8} -z^4 a^{-10} +17 z^4+a^3 z^3-5 a z^3-20 z^3 a^{-1} -22 z^3 a^{-3} -20 z^3 a^{-5} -11 z^3 a^{-7} +z^3 a^{-9} -3 a^2 z^2-13 z^2 a^{-2} +z^2 a^{-4} +2 z^2 a^{-6} -2 z^2 a^{-8} -13 z^2+a z+4 z a^{-1} +4 z a^{-3} +2 z a^{-5} +z a^{-7} +4 a^{-2} +2 a^{-4} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
