K13n1317
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n1317/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-15 t^2+30 t-37+30 t^{-1} -15 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | Data:K13n1317/Conway Polynomial |
| Determinant | 135 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-4} +2 z^6 a^{-6} -2 z^4 a^{-2} +7 z^4 a^{-4} +7 z^4 a^{-6} -3 z^4 a^{-8} -4 z^2 a^{-2} +9 z^2 a^{-4} +9 z^2 a^{-6} -9 z^2 a^{-8} +z^2 a^{-10} -2 a^{-2} +4 a^{-4} +4 a^{-6} -7 a^{-8} +2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +5 z^{10} a^{-6} +8 z^{10} a^{-8} +3 z^{10} a^{-10} +9 z^9 a^{-5} +14 z^9 a^{-7} +8 z^9 a^{-9} +3 z^9 a^{-11} +9 z^8 a^{-4} -3 z^8 a^{-6} -22 z^8 a^{-8} -9 z^8 a^{-10} +z^8 a^{-12} +5 z^7 a^{-3} -21 z^7 a^{-5} -60 z^7 a^{-7} -49 z^7 a^{-9} -15 z^7 a^{-11} +z^6 a^{-2} -20 z^6 a^{-4} -18 z^6 a^{-6} +8 z^6 a^{-8} -5 z^6 a^{-12} -5 z^5 a^{-3} +21 z^5 a^{-5} +83 z^5 a^{-7} +83 z^5 a^{-9} +26 z^5 a^{-11} +6 z^4 a^{-2} +24 z^4 a^{-4} +15 z^4 a^{-6} +4 z^4 a^{-8} +15 z^4 a^{-10} +8 z^4 a^{-12} +3 z^3 a^{-1} +8 z^3 a^{-3} -16 z^3 a^{-5} -66 z^3 a^{-7} -64 z^3 a^{-9} -19 z^3 a^{-11} -5 z^2 a^{-2} -14 z^2 a^{-4} -z^2 a^{-6} +6 z^2 a^{-8} -6 z^2 a^{-10} -4 z^2 a^{-12} -2 z a^{-1} -3 z a^{-3} +5 z a^{-5} +23 z a^{-7} +23 z a^{-9} +6 z a^{-11} +2 a^{-2} +4 a^{-4} -4 a^{-6} -7 a^{-8} -2 a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
