K12a1216

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^5-5 q^4+10 q^3-16 q^2+23 q-26+28 q^{-1} -26 q^{-2} +21 q^{-3} -14 q^{-4} +8 q^{-5} -4 q^{-6} + q^{-7} }[/math]
Alexander polynomial	[math]\displaystyle{ -2 t^4+11 t^3-25 t^2+35 t-37+35 t^{-1} -25 t^{-2} +11 t^{-3} -2 t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -2 z^8-5 z^6+z^4+2 z^2+1 }[/math]
Determinant	183
Signature	-2
HOMFLY-PT polynomial	[math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-4 a^2 z^6+z^6 a^{-2} -3 z^6+3 a^4 z^4-5 a^2 z^4+2 z^4 a^{-2} +z^4+a^4 z^2-4 a^2 z^2-2 z^2 a^{-2} +7 z^2-2 a^2-2 a^{-2} +5 }[/math]
Kauffman polynomial	[math]\displaystyle{ 4 a z^{11}+4 z^{11} a^{-1} +11 a^2 z^{10}+8 z^{10} a^{-2} +19 z^{10}+15 a^3 z^9+8 a z^9-2 z^9 a^{-1} +5 z^9 a^{-3} +15 a^4 z^8-21 a^2 z^8-33 z^8 a^{-2} +z^8 a^{-4} -70 z^8+12 a^5 z^7-30 a^3 z^7-59 a z^7-37 z^7 a^{-1} -20 z^7 a^{-3} +8 a^6 z^6-24 a^4 z^6-3 a^2 z^6+40 z^6 a^{-2} -3 z^6 a^{-4} +72 z^6+4 a^7 z^5-13 a^5 z^5+10 a^3 z^5+60 a z^5+55 z^5 a^{-1} +22 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+7 a^4 z^4+12 a^2 z^4-13 z^4 a^{-2} +2 z^4 a^{-4} -17 z^4-2 a^7 z^3+2 a^5 z^3+4 a^3 z^3-10 a z^3-14 z^3 a^{-1} -4 z^3 a^{-3} +a^6 z^2+a^4 z^2-5 a^2 z^2-4 z^2 a^{-2} -9 z^2-2 a^3 z-4 a z-4 z a^{-1} -2 z a^{-3} +2 a^2+2 a^{-2} +5 }[/math]

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.

Contents