K12a215

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^3-4 q^2+9 q-16+24 q^{-1} -28 q^{-2} +31 q^{-3} -29 q^{-4} +23 q^{-5} -16 q^{-6} +9 q^{-7} -4 q^{-8} + q^{-9} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+7 t^3-22 t^2+42 t-51+42 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -z^8-z^6+z^2+1 }[/math]
Determinant	195
Signature	-2
HOMFLY-PT polynomial	[math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-7 z^2 a^6-4 a^6+3 z^6 a^4+11 z^4 a^4+14 z^2 a^4+5 a^4-z^8 a^2-5 z^6 a^2-11 z^4 a^2-10 z^2 a^2-2 a^2+z^6+3 z^4+3 z^2+1 }[/math]
Kauffman polynomial	[math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+4 a^6 z^{10}+9 a^4 z^{10}+5 a^2 z^{10}+7 a^7 z^9+17 a^5 z^9+19 a^3 z^9+9 a z^9+7 a^8 z^8+9 a^6 z^8-a^4 z^8+5 a^2 z^8+8 z^8+4 a^9 z^7-7 a^7 z^7-40 a^5 z^7-52 a^3 z^7-19 a z^7+4 z^7 a^{-1} +a^{10} z^6-14 a^8 z^6-34 a^6 z^6-34 a^4 z^6-36 a^2 z^6+z^6 a^{-2} -20 z^6-9 a^9 z^5-6 a^7 z^5+36 a^5 z^5+56 a^3 z^5+14 a z^5-9 z^5 a^{-1} -2 a^{10} z^4+8 a^8 z^4+32 a^6 z^4+50 a^4 z^4+47 a^2 z^4-2 z^4 a^{-2} +17 z^4+6 a^9 z^3+6 a^7 z^3-18 a^5 z^3-27 a^3 z^3-5 a z^3+4 z^3 a^{-1} +a^{10} z^2-2 a^8 z^2-16 a^6 z^2-28 a^4 z^2-22 a^2 z^2-7 z^2-a^9 z-a^7 z+4 a^5 z+6 a^3 z+2 a z+a^8+4 a^6+5 a^4+2 a^2+1 }[/math]

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.

Contents