T(5,4): Difference between revisions

Revision as of 16:08, 26 August 2005

[[Image:T(7,3).{{{ext}}}|80px|link=T(7,3)]]

[[Image:T(15,2).{{{ext}}}|80px|link=T(15,2)]]

Visit T(5,4)'s page at the original Knot Atlas!

Planar diagram presentation	X_17,25,18,24 X_10,26,11,25 X_3,27,4,26 X_11,19,12,18 X_4,20,5,19 X_27,21,28,20 X_5,13,6,12 X_28,14,29,13 X_21,15,22,14 X_29,7,30,6 X_22,8,23,7 X_15,9,16,8 X_23,1,24,30 X_16,2,17,1 X_9,3,10,2
Gauss code	{14, 15, -3, -5, -7, 10, 11, 12, -15, -2, -4, 7, 8, 9, -12, -14, -1, 4, 5, 6, -9, -11, -13, 1, 2, 3, -6, -8, -10, 13}
Dowker-Thistlethwaite code	16 -26 -12 22 -2 -18 28 -8 -24 4 -14 -30 10 -20 -6

Jones polynomial	[math]\displaystyle{ - q^{-9} +2 q^{-8} -3 q^{-7} +3 q^{-6} -3 q^{-5} +3 q^{-4} - q^{-3} + q^{-2} }[/math]
Alexander polynomial	[math]\displaystyle{ 2 t^2-4 t+5-4 t^{-1} +2 t^{-2} }[/math]
Conway polynomial	[math]\displaystyle{ 2 z^4+4 z^2+1 }[/math]
Determinant	17
Signature	-4
HOMFLY-PT polynomial	[math]\displaystyle{ a^8 \left(-z^2\right)-a^8+a^6 z^4+2 a^6 z^2+a^4 z^4+3 a^4 z^2+2 a^4 }[/math]
Kauffman polynomial	[math]\displaystyle{ a^{11} z^3-a^{11} z+2 a^{10} z^4-2 a^{10} z^2+2 a^9 z^5-2 a^9 z^3+a^9 z+a^8 z^6+a^8 z^2-a^8+3 a^7 z^5-4 a^7 z^3+a^7 z+a^6 z^6-a^6 z^4+a^5 z^5-a^5 z^3-a^5 z+a^4 z^4-3 a^4 z^2+2 a^4 }[/math]
(other formats)

V₂ and V₃

(4, -8)

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