K13a510
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a510/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-17 t^2+42 t-55+42 t^{-1} -17 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | Data:K13a510/Conway Polynomial |
| Determinant | 179 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^6 a^{-6} +2 z^4 a^{-2} +2 z^4 a^{-6} -2 z^4 a^{-8} -z^4+3 z^2 a^{-2} -2 z^2 a^{-4} +4 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} -z^2+2 a^{-2} -2 a^{-4} +3 a^{-6} -3 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-6} +z^{12} a^{-8} +4 z^{11} a^{-5} +7 z^{11} a^{-7} +3 z^{11} a^{-9} +7 z^{10} a^{-4} +10 z^{10} a^{-6} +7 z^{10} a^{-8} +4 z^{10} a^{-10} +8 z^9 a^{-3} -3 z^9 a^{-5} -20 z^9 a^{-7} -6 z^9 a^{-9} +3 z^9 a^{-11} +8 z^8 a^{-2} -15 z^8 a^{-4} -51 z^8 a^{-6} -46 z^8 a^{-8} -17 z^8 a^{-10} +z^8 a^{-12} +7 z^7 a^{-1} -12 z^7 a^{-3} -18 z^7 a^{-5} -2 z^7 a^{-7} -18 z^7 a^{-9} -15 z^7 a^{-11} -9 z^6 a^{-2} +17 z^6 a^{-4} +83 z^6 a^{-6} +77 z^6 a^{-8} +19 z^6 a^{-10} -5 z^6 a^{-12} +4 z^6+a z^5-10 z^5 a^{-1} +6 z^5 a^{-3} +39 z^5 a^{-5} +47 z^5 a^{-7} +48 z^5 a^{-9} +23 z^5 a^{-11} -3 z^4 a^{-2} -14 z^4 a^{-4} -59 z^4 a^{-6} -57 z^4 a^{-8} -8 z^4 a^{-10} +7 z^4 a^{-12} -6 z^4-a z^3+2 z^3 a^{-1} -3 z^3 a^{-3} -26 z^3 a^{-5} -44 z^3 a^{-7} -39 z^3 a^{-9} -15 z^3 a^{-11} +5 z^2 a^{-2} +9 z^2 a^{-4} +20 z^2 a^{-6} +20 z^2 a^{-8} +3 z^2 a^{-10} -3 z^2 a^{-12} +2 z^2+2 z a^{-3} +6 z a^{-5} +11 z a^{-7} +11 z a^{-9} +4 z a^{-11} -2 a^{-2} -2 a^{-4} -3 a^{-6} -3 a^{-8} - a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
