K12a378
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+7 q^5-11 q^4+16 q^3-18 q^2+19 q-17+14 q^{-1} -10 q^{-2} +6 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-12 t^2+30 t-39+30 t^{-1} -12 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+1 }[/math] |
| Determinant | 127 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-2 a^2 z^4+2 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4+a^4 z^2-4 a^2 z^2+3 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} +2 z^2+a^4-2 a^2+2 a^{-2} - a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+4 z^{10} a^{-2} +7 z^{10}+3 a^3 z^9+6 a z^9+10 z^9 a^{-1} +7 z^9 a^{-3} +a^4 z^8-10 a^2 z^8-z^8 a^{-2} +8 z^8 a^{-4} -20 z^8-15 a^3 z^7-41 a z^7-44 z^7 a^{-1} -10 z^7 a^{-3} +8 z^7 a^{-5} -5 a^4 z^6+a^2 z^6-19 z^6 a^{-2} -7 z^6 a^{-4} +7 z^6 a^{-6} +z^6+24 a^3 z^5+63 a z^5+49 z^5 a^{-1} -6 z^5 a^{-5} +4 z^5 a^{-7} +8 a^4 z^4+18 a^2 z^4+16 z^4 a^{-2} -7 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +25 z^4-15 a^3 z^3-34 a z^3-20 z^3 a^{-1} -z^3 a^{-3} -3 z^3 a^{-5} -3 z^3 a^{-7} -5 a^4 z^2-14 a^2 z^2+6 z^2 a^{-4} +2 z^2 a^{-6} -13 z^2+3 a^3 z+6 a z+4 z a^{-1} +2 z a^{-3} +z a^{-5} +a^4+2 a^2-2 a^{-2} - a^{-4} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
