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Flat knot 6.1925

Min(phi) over symmetries of the knot is: [-2,-1,0,1,2,-1,1,1,2,0,1,1,0,1,-1]
Flat knots (up to 7 crossings) with same phi are :['6.1925', '7.11048', '7.41195']
Arrow polynomial of the knot is: 8*K1**3 - 4*K1*K2 - 4*K1 + 1
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.134', '6.409', '6.424', '6.534', '6.942', '6.969', '6.1192', '6.1280', '6.1310', '6.1325', '6.1858', '6.1925']
Outer characteristic polynomial of the knot is: t^6+35t^4+50t^2
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1925', '7.41195']
2-strand cable arrow polynomial of the knot is: -384*K1**2*K2**4 + 384*K1**2*K2**3 - 2848*K1**2*K2**2 + 1760*K1**2*K2 - 608*K1**2 + 256*K1*K2**3*K3 + 1632*K1*K2*K3 - 192*K2**6 + 128*K2**4*K4 - 1536*K2**4 - 32*K2**2*K3**2 - 16*K2**2*K4**2 + 896*K2**2*K4 + 336*K2**2 - 160*K3**2 - 80*K4**2 + 462
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1925']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.326', 'vk6.364', 'vk6.722', 'vk6.770', 'vk6.1459', 'vk6.1518', 'vk6.1959', 'vk6.1998', 'vk6.2457', 'vk6.2659', 'vk6.2999', 'vk6.3123', 'vk6.18397', 'vk6.18735', 'vk6.24858', 'vk6.25319', 'vk6.37058', 'vk6.44211', 'vk6.56168', 'vk6.60702']
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 O1O2O3U1U4U5O4O5O6U3U2U6
R3 orbit {'O1O2O3U1U4U5O4O5O6U3U2U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U2U3U4O5O6O4U1U6U5
Gauss code of K* O1O2O3U2U3U4O5O6O4U1U6U5
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 -2 0 0 -1 1 2],[ 2 0 2 1 2 2 2],[ 0 -2 0 0 -1 1 2],[ 0 -1 0 0 -1 1 1],[ 1 -2 1 1 0 1 2],[-1 -2 -1 -1 -1 0 2],[-2 -2 -2 -1 -2 -2 0]]
Primitive based matrix [[ 0 2 1 0 -1 -2],[-2 0 -2 -1 -2 -2],[-1 2 0 -1 -1 -2],[ 0 1 1 0 -1 -1],[ 1 2 1 1 0 -2],[ 2 2 2 1 2 0]]
If based matrix primitive False
Phi of primitive based matrix [-2,-1,0,1,2,2,1,2,2,1,1,2,1,1,2]
Phi over symmetry [-2,-1,0,1,2,-1,1,1,2,0,1,1,0,1,-1]
Phi of -K [-2,-1,0,1,2,-1,1,1,2,0,1,1,0,1,-1]
Phi of K* [-2,-1,0,1,2,-1,1,1,2,0,1,1,0,1,-1]
Phi of -K* [-2,-1,0,1,2,2,1,2,2,1,1,2,1,1,2]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial -z-1
Enhanced Jones-Krushkal polynomial -16w^3z+15w^2z-w
Inner characteristic polynomial t^5+25t^3+30t
Outer characteristic polynomial t^6+35t^4+50t^2
Flat arrow polynomial 8*K1**3 - 4*K1*K2 - 4*K1 + 1
2-strand cable arrow polynomial -384*K1**2*K2**4 + 384*K1**2*K2**3 - 2848*K1**2*K2**2 + 1760*K1**2*K2 - 608*K1**2 + 256*K1*K2**3*K3 + 1632*K1*K2*K3 - 192*K2**6 + 128*K2**4*K4 - 1536*K2**4 - 32*K2**2*K3**2 - 16*K2**2*K4**2 + 896*K2**2*K4 + 336*K2**2 - 160*K3**2 - 80*K4**2 + 462
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}]]
If K is slice True
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