K12a429
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+17 q^5-23 q^4+28 q^3-29 q^2+26 q-20+14 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-19 t^2+42 t-53+42 t^{-1} -19 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+5 z^4+2 z^2+1 }[/math] |
| Determinant | 183 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+4 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} +2 z^4-2 a^2 z^2+z^2 a^{-2} +z^2 a^{-4} -z^2 a^{-6} +3 z^2-a^2-2 a^{-2} +2 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +11 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10}+4 a z^9+4 z^9 a^{-1} +12 z^9 a^{-3} +12 z^9 a^{-5} +3 a^2 z^8-25 z^8 a^{-2} -3 z^8 a^{-4} +13 z^8 a^{-6} -6 z^8+a^3 z^7-9 a z^7-16 z^7 a^{-1} -35 z^7 a^{-3} -20 z^7 a^{-5} +9 z^7 a^{-7} -11 a^2 z^6+21 z^6 a^{-2} -13 z^6 a^{-4} -24 z^6 a^{-6} +4 z^6 a^{-8} -5 z^6-4 a^3 z^5-a z^5+7 z^5 a^{-1} +30 z^5 a^{-3} +12 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4-9 z^4 a^{-2} +17 z^4 a^{-4} +19 z^4 a^{-6} -4 z^4 a^{-8} +10 z^4+5 a^3 z^3+10 a z^3+3 z^3 a^{-1} -8 z^3 a^{-3} +z^3 a^{-5} +6 z^3 a^{-7} -z^3 a^{-9} -6 a^2 z^2-3 z^2 a^{-2} -8 z^2 a^{-4} -7 z^2 a^{-6} -8 z^2-2 a^3 z-4 a z-2 z a^{-1} -2 z a^{-5} -2 z a^{-7} +a^2+2 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. |
