K12a474

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^3-6 q^2+15 q-25+37 q^{-1} -44 q^{-2} +46 q^{-3} -42 q^{-4} +33 q^{-5} -22 q^{-6} +11 q^{-7} -4 q^{-8} + q^{-9} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+9 t^3-32 t^2+63 t-77+63 t^{-1} -32 t^{-2} +9 t^{-3} - t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -z^8+z^6+2 z^4+1 }[/math]
Determinant	287
Signature	-2
HOMFLY-PT polynomial	[math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-5 z^2 a^6-2 a^6+3 z^6 a^4+7 z^4 a^4+4 z^2 a^4-z^8 a^2-3 z^6 a^2-3 z^4 a^2+z^2 a^2+2 a^2+z^6+z^4-z^2 }[/math]
Kauffman polynomial	[math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+10 a^6 z^{10}+22 a^4 z^{10}+12 a^2 z^{10}+13 a^7 z^9+32 a^5 z^9+38 a^3 z^9+19 a z^9+9 a^8 z^8+2 a^6 z^8-13 a^4 z^8+9 a^2 z^8+15 z^8+4 a^9 z^7-22 a^7 z^7-83 a^5 z^7-92 a^3 z^7-29 a z^7+6 z^7 a^{-1} +a^{10} z^6-16 a^8 z^6-36 a^6 z^6-53 a^4 z^6-60 a^2 z^6+z^6 a^{-2} -25 z^6-7 a^9 z^5+18 a^7 z^5+73 a^5 z^5+61 a^3 z^5+7 a z^5-6 z^5 a^{-1} -2 a^{10} z^4+13 a^8 z^4+44 a^6 z^4+62 a^4 z^4+43 a^2 z^4+10 z^4+4 a^9 z^3-8 a^7 z^3-28 a^5 z^3-15 a^3 z^3+a z^3+a^{10} z^2-6 a^8 z^2-20 a^6 z^2-19 a^4 z^2-5 a^2 z^2+z^2-a^9 z+a^7 z+5 a^5 z+3 a^3 z+a^8+2 a^6-2 a^2 }[/math]

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.

Contents