K12a296

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^9-5 q^8+12 q^7-21 q^6+30 q^5-35 q^4+37 q^3-34 q^2+26 q-17+9 q^{-1} -3 q^{-2} + q^{-3} }[/math]
Alexander polynomial	[math]\displaystyle{ 3 t^3-21 t^2+55 t-73+55 t^{-1} -21 t^{-2} +3 t^{-3} }[/math]
Conway polynomial	[math]\displaystyle{ 3 z^6-3 z^4-2 z^2+1 }[/math]
Determinant	231
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -2 z^4 a^{-2} +4 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-6 z^2 a^{-2} +6 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} -z^2+a^2-4 a^{-2} +4 a^{-4} - a^{-6} +1 }[/math]
Kauffman polynomial	[math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +14 z^{10} a^{-4} +8 z^{10} a^{-6} +8 z^9 a^{-1} +19 z^9 a^{-3} +24 z^9 a^{-5} +13 z^9 a^{-7} +3 z^8 a^{-2} -8 z^8 a^{-4} +6 z^8 a^{-6} +11 z^8 a^{-8} +6 z^8+3 a z^7-13 z^7 a^{-1} -49 z^7 a^{-3} -58 z^7 a^{-5} -20 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-27 z^6 a^{-2} -36 z^6 a^{-4} -43 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -11 z^6-6 a z^5+12 z^5 a^{-1} +48 z^5 a^{-3} +41 z^5 a^{-5} +3 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+39 z^4 a^{-2} +54 z^4 a^{-4} +39 z^4 a^{-6} +12 z^4 a^{-8} -z^4 a^{-10} +8 z^4+3 a z^3-10 z^3 a^{-1} -23 z^3 a^{-3} -11 z^3 a^{-5} +2 z^3 a^{-7} +3 z^3 a^{-9} +3 a^2 z^2-24 z^2 a^{-2} -27 z^2 a^{-4} -13 z^2 a^{-6} -3 z^2 a^{-8} -4 z^2+4 z a^{-1} +6 z a^{-3} +2 z a^{-5} -a^2+4 a^{-2} +4 a^{-4} + a^{-6} +1 }[/math]

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.

Contents