K12n757
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-5 q^6+10 q^5-15 q^4+19 q^3-19 q^2+18 q-14+9 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-9 t^2+28 t-39+28 t^{-1} -9 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 115 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^4 a^{-2} -2 z^4 a^{-4} -2 z^4+a^2 z^2+z^2 a^{-6} -z^2- a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +6 z^9 a^{-1} +10 z^9 a^{-3} +4 z^9 a^{-5} +8 z^8 a^{-2} +3 z^8 a^{-4} +2 z^8 a^{-6} +7 z^8+4 a z^7-9 z^7 a^{-1} -22 z^7 a^{-3} -9 z^7 a^{-5} +a^2 z^6-26 z^6 a^{-2} -9 z^6 a^{-4} -16 z^6-9 a z^5-z^5 a^{-1} +23 z^5 a^{-3} +20 z^5 a^{-5} +5 z^5 a^{-7} -2 a^2 z^4+19 z^4 a^{-2} +11 z^4 a^{-4} +4 z^4 a^{-6} +z^4 a^{-8} +9 z^4+5 a z^3-2 z^3 a^{-1} -17 z^3 a^{-3} -14 z^3 a^{-5} -4 z^3 a^{-7} +a^2 z^2-8 z^2 a^{-2} -6 z^2 a^{-4} -3 z^2 a^{-6} -z^2 a^{-8} -3 z^2+2 z a^{-1} +5 z a^{-3} +3 z a^{-5} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
