K13a1067
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a1067/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+12 t^3-38 t^2+74 t-91+74 t^{-1} -38 t^{-2} +12 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1067/Conway Polynomial |
| Determinant | 343 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8+a^2 z^6-3 z^6 a^{-2} +2 z^6 a^{-4} -4 z^6+3 a^2 z^4-5 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} -8 z^4+4 a^2 z^2-4 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} -7 z^2+2 a^2- a^{-2} +3 a^{-4} - a^{-6} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12}+8 a z^{11}+20 z^{11} a^{-1} +12 z^{11} a^{-3} +8 a^2 z^{10}+30 z^{10} a^{-2} +22 z^{10} a^{-4} +16 z^{10}+4 a^3 z^9-19 a z^9-44 z^9 a^{-1} +5 z^9 a^{-3} +26 z^9 a^{-5} +a^4 z^8-29 a^2 z^8-100 z^8 a^{-2} -27 z^8 a^{-4} +22 z^8 a^{-6} -81 z^8-15 a^3 z^7+2 a z^7+6 z^7 a^{-1} -63 z^7 a^{-3} -39 z^7 a^{-5} +13 z^7 a^{-7} -4 a^4 z^6+36 a^2 z^6+90 z^6 a^{-2} -13 z^6 a^{-4} -30 z^6 a^{-6} +5 z^6 a^{-8} +108 z^6+18 a^3 z^5+15 a z^5+27 z^5 a^{-1} +56 z^5 a^{-3} +13 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +5 a^4 z^4-23 a^2 z^4-26 z^4 a^{-2} +27 z^4 a^{-4} +14 z^4 a^{-6} -2 z^4 a^{-8} -65 z^4-8 a^3 z^3-7 a z^3-10 z^3 a^{-1} -11 z^3 a^{-3} +3 z^3 a^{-5} +3 z^3 a^{-7} -2 a^4 z^2+10 a^2 z^2-z^2 a^{-2} -13 z^2 a^{-4} -4 z^2 a^{-6} +20 z^2+a^3 z-z a^{-1} -z a^{-3} -2 z a^{-5} -z a^{-7} -2 a^2+ a^{-2} +3 a^{-4} + a^{-6} -2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
