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Flat knot 6.935

Min(phi) over symmetries of the knot is: [-3,-1,0,0,1,3,0,1,2,0,3,0,0,1,0,0,0,1,0,2,0]
Flat knots (up to 7 crossings) with same phi are :['6.935', '7.16070']
Arrow polynomial of the knot is: -4*K1*K3 + 2*K2 + 2*K4 + 1
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.117', '6.935']
Outer characteristic polynomial of the knot is: t^7+84t^5+227t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.935', '7.16070']
2-strand cable arrow polynomial of the knot is: -1792*K1**2*K3**2 - 96*K1**2*K6**2 - 632*K1**2 + 2336*K1*K2*K3 + 1184*K1*K3*K4 + 96*K1*K5*K6 + 64*K1*K6*K7 - 1056*K2**2*K3**2 - 48*K2**2*K6**2 - 544*K2**2 + 672*K2*K3*K5 + 48*K2*K4*K6 + 32*K2*K6*K8 - 672*K3**2 - 156*K4**2 - 96*K5**2 - 48*K6**2 - 8*K7**2 - 4*K8**2 + 718
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.935']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.473', 'vk6.537', 'vk6.936', 'vk6.1033', 'vk6.1623', 'vk6.1724', 'vk6.2118', 'vk6.2221', 'vk6.2535', 'vk6.2836', 'vk6.3035', 'vk6.3167', 'vk6.20386', 'vk6.21729', 'vk6.27712', 'vk6.29258', 'vk6.39156', 'vk6.45884', 'vk6.57254', 'vk6.61893']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is -.
The reverse -K is
The mirror image K* is
The fillings (up to the first 10) associated to the algebraic genus:
Or click here to check the fillings

invariant value
Gauss code O1O2O3O4U5U6O5O6U1U3U2U4
R3 orbit {'O1O2O3O4U5U6O5O6U1U3U2U4'}
R3 orbit length 1
Gauss code of -K O1O2O3O4U1U3U2U4O5O6U5U6
Gauss code of K* O1O2O3O4U1U3U2U4O5O6U5U6
Gauss code of -K* Same
Diagrammatic symmetry type -
Flat genus of the diagram 2
If K is checkerboard colorable False
If K is almost classical False
Based matrix from Gauss code [[ 0 -3 0 0 3 -1 1],[ 3 0 2 1 3 2 4],[ 0 -2 0 0 2 -1 1],[ 0 -1 0 0 1 -1 1],[-3 -3 -2 -1 0 -4 -2],[ 1 -2 1 1 4 0 1],[-1 -4 -1 -1 2 -1 0]]
Primitive based matrix [[ 0 3 1 0 0 -1 -3],[-3 0 -2 -1 -2 -4 -3],[-1 2 0 -1 -1 -1 -4],[ 0 1 1 0 0 -1 -1],[ 0 2 1 0 0 -1 -2],[ 1 4 1 1 1 0 -2],[ 3 3 4 1 2 2 0]]
If based matrix primitive True
Phi of primitive based matrix [-3,-1,0,0,1,3,2,1,2,4,3,1,1,1,4,0,1,1,1,2,2]
Phi over symmetry [-3,-1,0,0,1,3,0,1,2,0,3,0,0,1,0,0,0,1,0,2,0]
Phi of -K [-3,-1,0,0,1,3,0,1,2,0,3,0,0,1,0,0,0,1,0,2,0]
Phi of K* [-3,-1,0,0,1,3,0,1,2,0,3,0,0,1,0,0,0,1,0,2,0]
Phi of -K* [-3,-1,0,0,1,3,2,1,2,4,3,1,1,1,4,0,1,1,1,2,2]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 7z+15
Enhanced Jones-Krushkal polynomial 4w^4z-6w^3z+9w^2z+15w
Inner characteristic polynomial t^6+64t^4+171t^2
Outer characteristic polynomial t^7+84t^5+227t^3
Flat arrow polynomial -4*K1*K3 + 2*K2 + 2*K4 + 1
2-strand cable arrow polynomial -1792*K1**2*K3**2 - 96*K1**2*K6**2 - 632*K1**2 + 2336*K1*K2*K3 + 1184*K1*K3*K4 + 96*K1*K5*K6 + 64*K1*K6*K7 - 1056*K2**2*K3**2 - 48*K2**2*K6**2 - 544*K2**2 + 672*K2*K3*K5 + 48*K2*K4*K6 + 32*K2*K6*K8 - 672*K3**2 - 156*K4**2 - 96*K5**2 - 48*K6**2 - 8*K7**2 - 4*K8**2 + 718
Genus of based matrix 0
Fillings of based matrix [[{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}]]
If K is slice True
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