K12a767
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-2 q^{10}+5 q^9-10 q^8+13 q^7-17 q^6+19 q^5-18 q^4+16 q^3-11 q^2+7 q-3+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -8 t^2+31 t-45+31 t^{-1} -8 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -8 z^4-z^2+1 }[/math] |
| Determinant | 123 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -3 z^4 a^{-4} -3 z^4 a^{-6} -z^4 a^{-8} +2 z^2 a^{-2} -2 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-10} +z^2+2 a^{-2} - a^{-6} - a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +5 z^{10} a^{-8} +2 z^{10} a^{-10} +6 z^9 a^{-5} +5 z^9 a^{-7} +z^9 a^{-9} +2 z^9 a^{-11} +8 z^8 a^{-4} +4 z^8 a^{-6} -11 z^8 a^{-8} -6 z^8 a^{-10} +z^8 a^{-12} +8 z^7 a^{-3} -4 z^7 a^{-5} -13 z^7 a^{-7} -11 z^7 a^{-9} -10 z^7 a^{-11} +6 z^6 a^{-2} -9 z^6 a^{-4} -24 z^6 a^{-6} -3 z^6 a^{-8} -6 z^6 a^{-12} +3 z^5 a^{-1} -10 z^5 a^{-3} -11 z^5 a^{-5} -7 z^5 a^{-7} +8 z^5 a^{-9} +17 z^5 a^{-11} -7 z^4 a^{-2} -z^4 a^{-4} +19 z^4 a^{-6} +10 z^4 a^{-8} +10 z^4 a^{-10} +12 z^4 a^{-12} +z^4-2 z^3 a^{-1} +6 z^3 a^{-3} +10 z^3 a^{-5} +15 z^3 a^{-7} +z^3 a^{-9} -12 z^3 a^{-11} +6 z^2 a^{-2} +4 z^2 a^{-4} -8 z^2 a^{-6} -z^2 a^{-8} -4 z^2 a^{-10} -8 z^2 a^{-12} -z^2-4 z a^{-5} -5 z a^{-7} +3 z a^{-9} +4 z a^{-11} -2 a^{-2} + a^{-6} - a^{-8} - a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
