K12a1244
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+6 q^5-10 q^4+14 q^3-17 q^2+18 q-16+14 q^{-1} -10 q^{-2} +6 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-16 t^2+22 t-23+22 t^{-1} -16 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-8 z^4-2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8+a^2 z^6-5 z^6 a^{-2} +z^6 a^{-4} -5 z^6+4 a^2 z^4-8 z^4 a^{-2} +4 z^4 a^{-4} -8 z^4+4 a^2 z^2-5 z^2 a^{-2} +4 z^2 a^{-4} -5 z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +4 a^2 z^{10}+5 z^{10} a^{-2} +9 z^{10}+3 a^3 z^9-3 a z^9+z^9 a^{-1} +7 z^9 a^{-3} +a^4 z^8-19 a^2 z^8-11 z^8 a^{-2} +8 z^8 a^{-4} -39 z^8-15 a^3 z^7-14 a z^7-21 z^7 a^{-1} -15 z^7 a^{-3} +7 z^7 a^{-5} -5 a^4 z^6+29 a^2 z^6+2 z^6 a^{-2} -17 z^6 a^{-4} +5 z^6 a^{-6} +58 z^6+23 a^3 z^5+30 a z^5+27 z^5 a^{-1} +6 z^5 a^{-3} -11 z^5 a^{-5} +3 z^5 a^{-7} +7 a^4 z^4-20 a^2 z^4+5 z^4 a^{-2} +15 z^4 a^{-4} -5 z^4 a^{-6} +z^4 a^{-8} -43 z^4-12 a^3 z^3-20 a z^3-14 z^3 a^{-1} +5 z^3 a^{-3} +8 z^3 a^{-5} -3 z^3 a^{-7} -2 a^4 z^2+8 a^2 z^2-4 z^2 a^{-2} -5 z^2 a^{-4} +z^2 a^{-6} -z^2 a^{-8} +13 z^2+2 a^3 z+4 a z+2 z a^{-1} -2 z a^{-3} -2 z a^{-5} -a^2+ a^{-2} + a^{-4} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
