K12a845

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^6+3 q^5-6 q^4+10 q^3-14 q^2+16 q-16+16 q^{-1} -12 q^{-2} +9 q^{-3} -5 q^{-4} +2 q^{-5} - q^{-6} }[/math]
Alexander polynomial	[math]\displaystyle{ 4 t^3-14 t^2+24 t-27+24 t^{-1} -14 t^{-2} +4 t^{-3} }[/math]
Conway polynomial	[math]\displaystyle{ 4 z^6+10 z^4+4 z^2+1 }[/math]
Determinant	111
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ a^2 z^6+z^6 a^{-2} +2 z^6-a^4 z^4+3 a^2 z^4+2 z^4 a^{-2} -z^4 a^{-4} +7 z^4-3 a^4 z^2+3 a^2 z^2-z^2 a^{-2} -2 z^2 a^{-4} +7 z^2-2 a^4+2 a^2-2 a^{-2} +3 }[/math]
Kauffman polynomial	[math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+7 a^2 z^{10}+5 z^{10}+a^5 z^9+a^3 z^9+11 a z^9+11 z^9 a^{-1} -12 a^4 z^8-31 a^2 z^8+15 z^8 a^{-2} -4 z^8-7 a^5 z^7-28 a^3 z^7-65 a z^7-30 z^7 a^{-1} +14 z^7 a^{-3} +25 a^4 z^6+36 a^2 z^6-43 z^6 a^{-2} +10 z^6 a^{-4} -42 z^6+18 a^5 z^5+70 a^3 z^5+98 a z^5+9 z^5 a^{-1} -31 z^5 a^{-3} +6 z^5 a^{-5} -21 a^4 z^4-3 a^2 z^4+33 z^4 a^{-2} -13 z^4 a^{-4} +3 z^4 a^{-6} +67 z^4-20 a^5 z^3-61 a^3 z^3-52 a z^3+9 z^3 a^{-1} +16 z^3 a^{-3} -3 z^3 a^{-5} +z^3 a^{-7} +7 a^4 z^2-5 a^2 z^2-13 z^2 a^{-2} +2 z^2 a^{-4} -27 z^2+8 a^5 z+17 a^3 z+11 a z-z a^{-1} -3 z a^{-3} -2 a^4-2 a^2+2 a^{-2} +3 }[/math]

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.

Contents