K12a462
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-13 q^3+19 q^2-23 q+25-23 q^{-1} +19 q^{-2} -13 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+19 t^2-32 t+39-32 t^{-1} +19 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-3 z^4-3 z^2+1 }[/math] |
| Determinant | 157 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-8 a^2 z^4-8 z^4 a^{-2} +z^4 a^{-4} +11 z^4+3 a^4 z^2-11 a^2 z^2-11 z^2 a^{-2} +3 z^2 a^{-4} +13 z^2+2 a^4-5 a^2-5 a^{-2} +2 a^{-4} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+5 a^3 z^9+8 a z^9+8 z^9 a^{-1} +5 z^9 a^{-3} +5 a^4 z^8+4 a^2 z^8+4 z^8 a^{-2} +5 z^8 a^{-4} -2 z^8+3 a^5 z^7-7 a^3 z^7-16 a z^7-16 z^7 a^{-1} -7 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-12 a^4 z^6-23 a^2 z^6-23 z^6 a^{-2} -12 z^6 a^{-4} +z^6 a^{-6} -20 z^6-8 a^5 z^5-2 a^3 z^5+6 a z^5+6 z^5 a^{-1} -2 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+10 a^4 z^4+32 a^2 z^4+32 z^4 a^{-2} +10 z^4 a^{-4} -3 z^4 a^{-6} +38 z^4+6 a^5 z^3+7 a^3 z^3+8 a z^3+8 z^3 a^{-1} +7 z^3 a^{-3} +6 z^3 a^{-5} +2 a^6 z^2-6 a^4 z^2-21 a^2 z^2-21 z^2 a^{-2} -6 z^2 a^{-4} +2 z^2 a^{-6} -26 z^2-2 a^5 z-4 a^3 z-5 a z-5 z a^{-1} -4 z a^{-3} -2 z a^{-5} +2 a^4+5 a^2+5 a^{-2} +2 a^{-4} +7 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
