K13a64
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a64/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+14 t^3-44 t^2+82 t-99+82 t^{-1} -44 t^{-2} +14 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a64/Conway Polynomial |
| Determinant | 383 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -3 z^6 a^{-2} -2 z^6 a^{-4} +z^6 a^{-6} +2 z^6-a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +z^4 a^{-6} +6 z^4-2 a^2 z^2-11 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +8 z^2-a^2-6 a^{-2} +4 a^{-4} - a^{-6} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +6 z^{11} a^{-1} +16 z^{11} a^{-3} +10 z^{11} a^{-5} +23 z^{10} a^{-2} +36 z^{10} a^{-4} +21 z^{10} a^{-6} +8 z^{10}+7 a z^9+8 z^9 a^{-1} +z^9 a^{-3} +24 z^9 a^{-5} +24 z^9 a^{-7} +4 a^2 z^8-49 z^8 a^{-2} -73 z^8 a^{-4} -19 z^8 a^{-6} +16 z^8 a^{-8} -7 z^8+a^3 z^7-15 a z^7-41 z^7 a^{-1} -66 z^7 a^{-3} -86 z^7 a^{-5} -39 z^7 a^{-7} +6 z^7 a^{-9} -12 a^2 z^6+15 z^6 a^{-2} +25 z^6 a^{-4} -21 z^6 a^{-6} -23 z^6 a^{-8} +z^6 a^{-10} -19 z^6-3 a^3 z^5+7 a z^5+39 z^5 a^{-1} +73 z^5 a^{-3} +64 z^5 a^{-5} +15 z^5 a^{-7} -5 z^5 a^{-9} +13 a^2 z^4+31 z^4 a^{-2} +25 z^4 a^{-4} +21 z^4 a^{-6} +7 z^4 a^{-8} +33 z^4+3 a^3 z^3+3 a z^3-11 z^3 a^{-1} -21 z^3 a^{-3} -11 z^3 a^{-5} -z^3 a^{-7} -6 a^2 z^2-27 z^2 a^{-2} -18 z^2 a^{-4} -5 z^2 a^{-6} -20 z^2-a^3 z-2 a z-z a^{-1} -z a^{-3} -2 z a^{-5} -z a^{-7} +a^2+6 a^{-2} +4 a^{-4} + a^{-6} +5 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
