K12a790

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^8+4 q^7-9 q^6+14 q^5-19 q^4+22 q^3-22 q^2+20 q-14+10 q^{-1} -5 q^{-2} +2 q^{-3} - q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ 4 t^3-16 t^2+32 t-39+32 t^{-1} -16 t^{-2} +4 t^{-3} }[/math]
Conway polynomial	[math]\displaystyle{ 4 z^6+8 z^4+4 z^2+1 }[/math]
Determinant	143
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+6 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} +3 z^4-3 a^2 z^2+6 z^2 a^{-2} -2 z^2 a^{-4} -z^2 a^{-6} +4 z^2-2 a^2+2 a^{-2} -2 a^{-4} +3 }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +6 z^{10} a^{-2} +4 z^{10} a^{-4} +2 z^{10}+2 a z^9+2 z^9 a^{-1} +8 z^9 a^{-3} +8 z^9 a^{-5} +2 a^2 z^8-15 z^8 a^{-2} +10 z^8 a^{-6} -3 z^8+a^3 z^7-3 a z^7-6 z^7 a^{-1} -23 z^7 a^{-3} -13 z^7 a^{-5} +8 z^7 a^{-7} -8 a^2 z^6+23 z^6 a^{-2} -8 z^6 a^{-4} -19 z^6 a^{-6} +4 z^6 a^{-8} -5 a^3 z^5-8 a z^5+z^5 a^{-1} +28 z^5 a^{-3} +10 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +10 a^2 z^4-25 z^4 a^{-2} +6 z^4 a^{-4} +14 z^4 a^{-6} -5 z^4 a^{-8} -2 z^4+8 a^3 z^3+16 a z^3+z^3 a^{-1} -17 z^3 a^{-3} -4 z^3 a^{-5} +5 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2+11 z^2 a^{-2} +3 z^2 a^{-4} -4 z^2 a^{-6} -z^2-4 a^3 z-7 a z-2 z a^{-1} +4 z a^{-3} +2 z a^{-5} -z a^{-7} +2 a^2-2 a^{-2} -2 a^{-4} +3 }[/math]

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.

Contents