K12a123

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^2-3 q+7-12 q^{-1} +18 q^{-2} -21 q^{-3} +23 q^{-4} -22 q^{-5} +18 q^{-6} -13 q^{-7} +7 q^{-8} -3 q^{-9} + q^{-10} }[/math]
Alexander polynomial	[math]\displaystyle{ t^4-7 t^3+19 t^2-30 t+35-30 t^{-1} +19 t^{-2} -7 t^{-3} + t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ z^8+z^6-3 z^4-z^2+1 }[/math]
Determinant	149
Signature	-4
HOMFLY-PT polynomial	[math]\displaystyle{ z^4 a^8+3 z^2 a^8+2 a^8-2 z^6 a^6-8 z^4 a^6-11 z^2 a^6-6 a^6+z^8 a^4+5 z^6 a^4+11 z^4 a^4+14 z^2 a^4+7 a^4-2 z^6 a^2-8 z^4 a^2-10 z^2 a^2-4 a^2+z^4+3 z^2+2 }[/math]
Kauffman polynomial	[math]\displaystyle{ z^4 a^{12}-z^2 a^{12}+3 z^5 a^{11}-2 z^3 a^{11}+6 z^6 a^{10}-5 z^4 a^{10}+2 z^2 a^{10}+10 z^7 a^9-16 z^5 a^9+14 z^3 a^9-4 z a^9+12 z^8 a^8-23 z^6 a^8+18 z^4 a^8-7 z^2 a^8+2 a^8+10 z^9 a^7-15 z^7 a^7-6 z^5 a^7+15 z^3 a^7-6 z a^7+5 z^{10} a^6+5 z^8 a^6-48 z^6 a^6+56 z^4 a^6-28 z^2 a^6+6 a^6+z^{11} a^5+16 z^9 a^5-59 z^7 a^5+56 z^5 a^5-19 z^3 a^5+z a^5+8 z^{10} a^4-15 z^8 a^4-23 z^6 a^4+54 z^4 a^4-32 z^2 a^4+7 a^4+z^{11} a^3+9 z^9 a^3-48 z^7 a^3+65 z^5 a^3-31 z^3 a^3+5 z a^3+3 z^{10} a^2-7 z^8 a^2-9 z^6 a^2+31 z^4 a^2-21 z^2 a^2+4 a^2+3 z^9 a-14 z^7 a+22 z^5 a-13 z^3 a+2 z a+z^8-5 z^6+9 z^4-7 z^2+2 }[/math]

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.

Contents