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Flat knot 6.1280

Min(phi) over symmetries of the knot is: [-2,-1,0,1,2,0,1,0,2,1,1,0,1,1,0]
Flat knots (up to 7 crossings) with same phi are :['6.1280', '7.22157', '7.37185']
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+19t^4+34t^2
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1280', '7.37185']
2-strand cable arrow polynomial of the knot is: -896*K1**2*K2**4 + 640*K1**2*K2**3 - 3744*K1**2*K2**2 + 2208*K1**2*K2 - 608*K1**2 + 512*K1*K2**3*K3 + 2080*K1*K2*K3 - 704*K2**6 + 384*K2**4*K4 - 2176*K2**4 - 32*K2**2*K3**2 - 16*K2**2*K4**2 + 1344*K2**2*K4 + 784*K2**2 - 160*K3**2 - 80*K4**2 + 462
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1280']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.324', 'vk6.363', 'vk6.718', 'vk6.765', 'vk6.1452', 'vk6.1511', 'vk6.1954', 'vk6.1993', 'vk6.2462', 'vk6.2665', 'vk6.3003', 'vk6.3125', 'vk6.18394', 'vk6.18734', 'vk6.24853', 'vk6.25314', 'vk6.37049', 'vk6.44204', 'vk6.56171', 'vk6.60705']
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 O1O2O3U1O4O5U4U5O6U3U2U6
R3 orbit {'O1O2O3U1O4O5U4U5O6U3U2U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U2U1O4U5U6O5O6U3
Gauss code of K* O1O2O3U4U2U1O4U5U6O5O6U3
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 0 0 2],[ 0 -2 0 0 -1 1 2],[ 0 -1 0 0 -1 1 1],[ 1 0 1 1 0 1 0],[-1 0 -1 -1 -1 0 0],[-2 -2 -2 -1 0 0 0]]
Primitive based matrix [[ 0 2 1 0 -1 -2],[-2 0 0 -1 0 -2],[-1 0 0 -1 -1 0],[ 0 1 1 0 -1 -1],[ 1 0 1 1 0 0],[ 2 2 0 1 0 0]]
If based matrix primitive False
Phi of primitive based matrix [-2,-1,0,1,2,0,1,0,2,1,1,0,1,1,0]
Phi over symmetry [-2,-1,0,1,2,0,1,0,2,1,1,0,1,1,0]
Phi of -K [-2,-1,0,1,2,1,1,3,2,0,1,3,0,1,1]
Phi of K* [-2,-1,0,1,2,1,1,3,2,0,1,3,0,1,1]
Phi of -K* [-2,-1,0,1,2,0,1,0,2,1,1,0,1,1,0]
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+9t^3+14t
Outer characteristic polynomial t^6+19t^4+34t^2
Flat arrow polynomial 8*K1**3 - 4*K1*K2 - 4*K1 + 1
2-strand cable arrow polynomial -896*K1**2*K2**4 + 640*K1**2*K2**3 - 3744*K1**2*K2**2 + 2208*K1**2*K2 - 608*K1**2 + 512*K1*K2**3*K3 + 2080*K1*K2*K3 - 704*K2**6 + 384*K2**4*K4 - 2176*K2**4 - 32*K2**2*K3**2 - 16*K2**2*K4**2 + 1344*K2**2*K4 + 784*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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