K12a1141
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-9 q^6+15 q^5-21 q^4+25 q^3-26 q^2+24 q-18+13 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-22 t^2+34 t-37+34 t^{-1} -22 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+6 z^4+2 z^2+1 }[/math] |
| Determinant | 167 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-5 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +7 z^4-3 a^2 z^2-2 z^2 a^{-2} +3 z^2 a^{-4} -2 z^2 a^{-6} +6 z^2-a^2+ a^{-2} - a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +11 z^{10} a^{-2} +6 z^{10} a^{-4} +5 z^{10}+5 a z^9+5 z^9 a^{-1} +9 z^9 a^{-3} +9 z^9 a^{-5} +3 a^2 z^8-32 z^8 a^{-2} -5 z^8 a^{-4} +10 z^8 a^{-6} -14 z^8+a^3 z^7-17 a z^7-33 z^7 a^{-1} -35 z^7 a^{-3} -12 z^7 a^{-5} +8 z^7 a^{-7} -11 a^2 z^6+35 z^6 a^{-2} -4 z^6 a^{-4} -15 z^6 a^{-6} +4 z^6 a^{-8} +9 z^6-4 a^3 z^5+16 a z^5+46 z^5 a^{-1} +43 z^5 a^{-3} +4 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4-18 z^4 a^{-2} +5 z^4 a^{-4} +7 z^4 a^{-6} -5 z^4 a^{-8} +4 a^3 z^3-6 a z^3-24 z^3 a^{-1} -20 z^3 a^{-3} +5 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2+6 z^2 a^{-2} +z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} -3 z^2-a^3 z+3 z a^{-1} +3 z a^{-3} -z a^{-7} +a^2- a^{-2} - a^{-4} +2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
