K12n14

From Knot Atlas
Jump to navigationJump to search

Polynomial invariants

Jones polynomial [math]\displaystyle{ q^6-4 q^5+8 q^4-11 q^3+14 q^2-15 q+14-11 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math]
Alexander polynomial [math]\displaystyle{ -t^3+7 t^2-21 t+31-21 t^{-1} +7 t^{-2} - t^{-3} }[/math]
Conway polynomial [math]\displaystyle{ -z^6+z^4-2 z^2+1 }[/math]
Determinant 89
Signature 0
HOMFLY-PT polynomial [math]\displaystyle{ -z^6 a^{-2} -3 z^4 a^{-2} +z^4 a^{-4} +3 z^4-3 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +5 z^2+a^4-2 a^2-2 a^{-2} + a^{-4} +3 }[/math]
Kauffman polynomial [math]\displaystyle{ z^{10} a^{-2} +z^{10}+2 a z^9+6 z^9 a^{-1} +4 z^9 a^{-3} +a^2 z^8+8 z^8 a^{-2} +6 z^8 a^{-4} +3 z^8-5 a z^7-13 z^7 a^{-1} -4 z^7 a^{-3} +4 z^7 a^{-5} -a^2 z^6-28 z^6 a^{-2} -15 z^6 a^{-4} +z^6 a^{-6} -13 z^6+3 a^3 z^5+12 a z^5+8 z^5 a^{-1} -11 z^5 a^{-3} -10 z^5 a^{-5} +a^4 z^4+7 a^2 z^4+27 z^4 a^{-2} +7 z^4 a^{-4} -2 z^4 a^{-6} +24 z^4-4 a^3 z^3-6 a z^3+3 z^3 a^{-1} +10 z^3 a^{-3} +5 z^3 a^{-5} -2 a^4 z^2-8 a^2 z^2-11 z^2 a^{-2} -2 z^2 a^{-4} +z^2 a^{-6} -14 z^2+a^3 z-2 z a^{-1} -2 z a^{-3} -z a^{-5} +a^4+2 a^2+2 a^{-2} + a^{-4} +3 }[/math]



Modifying This Page

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.