K12n346

Dowker-Thistlethwaite code

4 10 14 16 2 -20 8 6 -22 -24 -12 -18

Jones polynomial	[math]\displaystyle{ -q^7+2 q^6-3 q^5+3 q^4-3 q^3+3 q^2-q+1+ q^{-1} - q^{-2} + q^{-3} - q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ t^4-2 t^3+2 t^2-t+1- t^{-1} +2 t^{-2} -2 t^{-3} + t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ z^8+6 z^6+10 z^4+5 z^2+1 }[/math]
Determinant	13
Signature	0
HOMFLY-PT polynomial	[math]\displaystyle{ z^8 a^{-2} +7 z^6 a^{-2} -z^6 a^{-4} -a^2 z^4+16 z^4 a^{-2} -5 z^4 a^{-4} -3 a^2 z^2+14 z^2 a^{-2} -7 z^2 a^{-4} +z^2-2 a^2+4 a^{-2} -3 a^{-4} +2 }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^9 a^{-1} +3 z^9 a^{-3} +2 z^9 a^{-5} +a^2 z^8-7 z^8 a^{-2} -4 z^8 a^{-4} +2 z^8 a^{-6} +a^3 z^7+a z^7-8 z^7 a^{-1} -19 z^7 a^{-3} -10 z^7 a^{-5} +z^7 a^{-7} -6 a^2 z^6+16 z^6 a^{-2} +z^6 a^{-4} -10 z^6 a^{-6} -z^6-6 a^3 z^5-7 a z^5+18 z^5 a^{-1} +36 z^5 a^{-3} +12 z^5 a^{-5} -5 z^5 a^{-7} +10 a^2 z^4-20 z^4 a^{-2} +z^4 a^{-4} +12 z^4 a^{-6} +z^4+10 a^3 z^3+11 a z^3-16 z^3 a^{-1} -28 z^3 a^{-3} -5 z^3 a^{-5} +6 z^3 a^{-7} -6 a^2 z^2+13 z^2 a^{-2} +5 z^2 a^{-4} -4 z^2 a^{-6} -2 z^2-4 a^3 z-5 a z+3 z a^{-1} +8 z a^{-3} +2 z a^{-5} -2 z a^{-7} +2 a^2-4 a^{-2} -3 a^{-4} +2 }[/math]

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.

Contents