K12n234
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-2 q^{12}+3 q^{11}-5 q^{10}+6 q^9-7 q^8+6 q^7-5 q^6+4 q^5-2 q^4+2 q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-6 t^2+7 t-7+7 t^{-1} -6 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-2 z^4+3 z^2+1 }[/math] |
| Determinant | 43 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-8} +2 z^6 a^{-6} -7 z^6 a^{-8} +z^6 a^{-10} +11 z^4 a^{-6} -18 z^4 a^{-8} +5 z^4 a^{-10} +17 z^2 a^{-6} -21 z^2 a^{-8} +7 z^2 a^{-10} +7 a^{-6} -9 a^{-8} +3 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-8} +z^{10} a^{-10} +z^9 a^{-7} +3 z^9 a^{-9} +2 z^9 a^{-11} -6 z^8 a^{-8} -4 z^8 a^{-10} +2 z^8 a^{-12} -5 z^7 a^{-7} -16 z^7 a^{-9} -9 z^7 a^{-11} +2 z^7 a^{-13} +3 z^6 a^{-6} +18 z^6 a^{-8} +7 z^6 a^{-10} -6 z^6 a^{-12} +2 z^6 a^{-14} +10 z^5 a^{-7} +33 z^5 a^{-9} +17 z^5 a^{-11} -4 z^5 a^{-13} +2 z^5 a^{-15} -15 z^4 a^{-6} -34 z^4 a^{-8} -7 z^4 a^{-10} +8 z^4 a^{-12} -3 z^4 a^{-14} +z^4 a^{-16} -14 z^3 a^{-7} -33 z^3 a^{-9} -11 z^3 a^{-11} +4 z^3 a^{-13} -4 z^3 a^{-15} +20 z^2 a^{-6} +29 z^2 a^{-8} +5 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} -2 z^2 a^{-16} +8 z a^{-7} +11 z a^{-9} +2 z a^{-11} +z a^{-15} -7 a^{-6} -9 a^{-8} -3 a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
