K12a745
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-2 q^{10}+3 q^9-5 q^8+6 q^7-7 q^6+8 q^5-8 q^4+7 q^3-5 q^2+4 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^2+15 t-21+15 t^{-1} -4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^4-z^2+1 }[/math] |
| Determinant | 59 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -z^4 a^{-4} -z^4 a^{-6} -z^4 a^{-8} -z^2 a^{-2} -2 z^2 a^{-8} +z^2 a^{-10} +z^2+ a^{-6} -2 a^{-8} + a^{-10} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +4 z^{10} a^{-8} +2 z^{10} a^{-10} +2 z^9 a^{-5} -3 z^9 a^{-7} -3 z^9 a^{-9} +2 z^9 a^{-11} +2 z^8 a^{-4} -9 z^8 a^{-6} -23 z^8 a^{-8} -11 z^8 a^{-10} +z^8 a^{-12} +2 z^7 a^{-3} -6 z^7 a^{-5} -z^7 a^{-7} -5 z^7 a^{-9} -12 z^7 a^{-11} +2 z^6 a^{-2} -4 z^6 a^{-4} +16 z^6 a^{-6} +46 z^6 a^{-8} +18 z^6 a^{-10} -6 z^6 a^{-12} +2 z^5 a^{-1} -2 z^5 a^{-3} +6 z^5 a^{-5} +9 z^5 a^{-7} +21 z^5 a^{-9} +22 z^5 a^{-11} -z^4 a^{-2} +4 z^4 a^{-4} -15 z^4 a^{-6} -43 z^4 a^{-8} -12 z^4 a^{-10} +10 z^4 a^{-12} +z^4-3 z^3 a^{-1} +z^3 a^{-3} -11 z^3 a^{-7} -22 z^3 a^{-9} -15 z^3 a^{-11} -2 z^2 a^{-2} +7 z^2 a^{-6} +16 z^2 a^{-8} +5 z^2 a^{-10} -4 z^2 a^{-12} -2 z^2+3 z a^{-7} +7 z a^{-9} +4 z a^{-11} - a^{-6} -2 a^{-8} - a^{-10} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
