K13n3753
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n3753/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^5+3 t^4-3 t^3+6 t-9+6 t^{-1} -3 t^{-3} +3 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | Data:K13n3753/Conway Polynomial |
| Determinant | 7 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -9 z^8 a^{-4} +z^8 a^{-6} +7 z^6 a^{-2} -30 z^6 a^{-4} +9 z^6 a^{-6} +16 z^4 a^{-2} -48 z^4 a^{-4} +26 z^4 a^{-6} -2 z^4 a^{-8} +15 z^2 a^{-2} -37 z^2 a^{-4} +30 z^2 a^{-6} -6 z^2 a^{-8} +5 a^{-2} -11 a^{-4} +11 a^{-6} -4 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +4 z^{10} a^{-4} +2 z^{10} a^{-6} +2 z^9 a^{-1} -4 z^9 a^{-3} -6 z^9 a^{-5} +z^9 a^{-7} +z^9 a^{-9} -12 z^8 a^{-2} -31 z^8 a^{-4} -18 z^8 a^{-6} +2 z^8 a^{-8} +2 z^8 a^{-10} +z^8-12 z^7 a^{-1} -5 z^7 a^{-3} +4 z^7 a^{-5} -7 z^7 a^{-7} -3 z^7 a^{-9} +z^7 a^{-11} +20 z^6 a^{-2} +78 z^6 a^{-4} +55 z^6 a^{-6} -7 z^6 a^{-8} -10 z^6 a^{-10} -6 z^6+20 z^5 a^{-1} +25 z^5 a^{-3} +18 z^5 a^{-5} +17 z^5 a^{-7} -z^5 a^{-9} -5 z^5 a^{-11} -16 z^4 a^{-2} -90 z^4 a^{-4} -78 z^4 a^{-6} +14 z^4 a^{-10} +10 z^4-12 z^3 a^{-1} -22 z^3 a^{-3} -29 z^3 a^{-5} -23 z^3 a^{-7} +3 z^3 a^{-9} +7 z^3 a^{-11} +13 z^2 a^{-2} +52 z^2 a^{-4} +47 z^2 a^{-6} +8 z^2 a^{-8} -5 z^2 a^{-10} -5 z^2+3 z a^{-1} +8 z a^{-3} +10 z a^{-5} +8 z a^{-7} +z a^{-9} -2 z a^{-11} -5 a^{-2} -11 a^{-4} -11 a^{-6} -4 a^{-8} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
