K12a1142
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+3 q^5-6 q^4+10 q^3-12 q^2+14 q-15+13 q^{-1} -10 q^{-2} +8 q^{-3} -4 q^{-4} +2 q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-14 t^2+21 t-21+21 t^{-1} -14 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+10 z^4+z^2+1 }[/math] |
| Determinant | 99 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^6+z^6 a^{-2} +2 z^6-a^4 z^4+3 a^2 z^4+2 z^4 a^{-2} -z^4 a^{-4} +7 z^4-3 a^4 z^2+2 a^2 z^2-z^2 a^{-2} -2 z^2 a^{-4} +5 z^2-a^4+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+6 a^2 z^{10}+4 z^{10}+a^5 z^9-a^3 z^9+6 a z^9+8 z^9 a^{-1} -13 a^4 z^8-30 a^2 z^8+11 z^8 a^{-2} -6 z^8-7 a^5 z^7-17 a^3 z^7-42 a z^7-20 z^7 a^{-1} +12 z^7 a^{-3} +30 a^4 z^6+48 a^2 z^6-26 z^6 a^{-2} +10 z^6 a^{-4} -18 z^6+17 a^5 z^5+47 a^3 z^5+65 a z^5+4 z^5 a^{-1} -25 z^5 a^{-3} +6 z^5 a^{-5} -30 a^4 z^4-31 a^2 z^4+10 z^4 a^{-2} -15 z^4 a^{-4} +3 z^4 a^{-6} +27 z^4-16 a^5 z^3-38 a^3 z^3-32 a z^3+6 z^3 a^{-1} +12 z^3 a^{-3} -3 z^3 a^{-5} +z^3 a^{-7} +13 a^4 z^2+13 a^2 z^2+6 z^2 a^{-4} -6 z^2+4 a^5 z+8 a^3 z+3 a z-3 z a^{-1} -2 z a^{-3} -a^4-2 a^2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
