K12a294
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-10 q^{-1} +18 q^{-2} -24 q^{-3} +30 q^{-4} -31 q^{-5} +29 q^{-6} -23 q^{-7} +15 q^{-8} -8 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+24 t^2-40 t+47-40 t^{-1} +24 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+10 z^4+7 z^2+1 }[/math] |
| Determinant | 197 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-6 z^2 a^8-3 a^8+z^8 a^6+5 z^6 a^6+11 z^4 a^6+11 z^2 a^6+3 a^6+z^8 a^4+4 z^6 a^4+6 z^4 a^4+5 z^2 a^4+2 a^4-z^6 a^2-3 z^4 a^2-3 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+6 z^7 a^{11}-8 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+9 z^8 a^{10}-14 z^6 a^{10}+13 z^4 a^{10}-5 z^2 a^{10}+10 z^9 a^9-16 z^7 a^9+14 z^5 a^9-4 z^3 a^9+z a^9+7 z^{10} a^8-3 z^8 a^8-12 z^6 a^8+12 z^4 a^8+3 z^2 a^8-3 a^8+2 z^{11} a^7+17 z^9 a^7-53 z^7 a^7+54 z^5 a^7-26 z^3 a^7+6 z a^7+13 z^{10} a^6-22 z^8 a^6-2 z^6 a^6+7 z^4 a^6+4 z^2 a^6-3 a^6+2 z^{11} a^5+14 z^9 a^5-50 z^7 a^5+44 z^5 a^5-17 z^3 a^5+2 z a^5+6 z^{10} a^4-6 z^8 a^4-19 z^6 a^4+24 z^4 a^4-10 z^2 a^4+2 a^4+7 z^9 a^3-18 z^7 a^3+10 z^5 a^3+z^3 a^3-z a^3+4 z^8 a^2-12 z^6 a^2+12 z^4 a^2-5 z^2 a^2+a^2+z^7 a-3 z^5 a+3 z^3 a-z a }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
