K13a1000
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a1000/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^4+10 t^3-40 t^2+86 t-109+86 t^{-1} -40 t^{-2} +10 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | Data:K13a1000/Conway Polynomial |
| Determinant | 383 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +3 z^6 a^{-4} +2 z^6-a^2 z^4-6 z^4 a^{-2} +5 z^4 a^{-4} -3 z^4 a^{-6} +5 z^4-2 a^2 z^2-4 z^2 a^{-2} +z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} +6 z^2-a^2-2 a^{-4} + a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +7 z^{11} a^{-1} +16 z^{11} a^{-3} +9 z^{11} a^{-5} +27 z^{10} a^{-2} +35 z^{10} a^{-4} +18 z^{10} a^{-6} +10 z^{10}+8 a z^9+8 z^9 a^{-1} +6 z^9 a^{-3} +26 z^9 a^{-5} +20 z^9 a^{-7} +4 a^2 z^8-63 z^8 a^{-2} -70 z^8 a^{-4} -13 z^8 a^{-6} +13 z^8 a^{-8} -15 z^8+a^3 z^7-18 a z^7-48 z^7 a^{-1} -83 z^7 a^{-3} -93 z^7 a^{-5} -34 z^7 a^{-7} +5 z^7 a^{-9} -11 a^2 z^6+40 z^6 a^{-2} +29 z^6 a^{-4} -24 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -2 z^6-3 a^3 z^5+12 a z^5+51 z^5 a^{-1} +95 z^5 a^{-3} +89 z^5 a^{-5} +24 z^5 a^{-7} -6 z^5 a^{-9} +11 a^2 z^4-6 z^4 a^{-2} +4 z^4 a^{-4} +27 z^4 a^{-6} +14 z^4 a^{-8} -z^4 a^{-10} +13 z^4+3 a^3 z^3-a z^3-21 z^3 a^{-1} -41 z^3 a^{-3} -38 z^3 a^{-5} -12 z^3 a^{-7} +2 z^3 a^{-9} -5 a^2 z^2-z^2 a^{-2} +2 z^2 a^{-4} -6 z^2 a^{-6} -5 z^2 a^{-8} -9 z^2-a^3 z-a z+2 z a^{-1} +6 z a^{-3} +7 z a^{-5} +3 z a^{-7} +a^2-2 a^{-4} - a^{-6} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
