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Flat knot 6.1932

Min(phi) over symmetries of the knot is: [-2,-1,1,2,-1,2,3,2,2,-1]
Flat knots (up to 7 crossings) with same phi are :['6.1931', '6.1932', '7.40268', '7.40283']
Arrow polynomial of the knot is: -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.65', '6.137', '6.201', '6.203', '6.214', '6.310', '6.314', '6.332', '6.385', '6.386', '6.401', '6.516', '6.564', '6.571', '6.572', '6.578', '6.621', '6.626', '6.716', '6.773', '6.807', '6.814', '6.821', '6.940', '6.966', '6.1036', '6.1071', '6.1108', '6.1111', '6.1131', '6.1188', '6.1203', '6.1206', '6.1220', '6.1340', '6.1387', '6.1548', '6.1663', '6.1680', '6.1693', '6.1831', '6.1932']
Outer characteristic polynomial of the knot is: t^5+21t^3+45t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1931', '6.1932']
2-strand cable arrow polynomial of the knot is: -32*K1**4 - 768*K1**2*K2**2 + 768*K1**2*K2 - 32*K1**2*K3**2 - 1544*K1**2 + 320*K1*K2**3*K3 + 2560*K1*K2*K3 + 256*K1*K3*K4 + 64*K1*K4*K5 - 400*K2**4 - 800*K2**2*K3**2 - 16*K2**2*K4**2 + 144*K2**2*K4 - 1036*K2**2 + 528*K2*K3*K5 + 32*K2*K4*K6 - 1184*K3**2 - 172*K4**2 - 136*K5**2 - 12*K6**2 + 1458
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1932']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.72626', 'vk6.72777', 'vk6.73092', 'vk6.73171', 'vk6.73817', 'vk6.73948', 'vk6.73969', 'vk6.75759', 'vk6.75800', 'vk6.77874', 'vk6.77928', 'vk6.77988', 'vk6.78017', 'vk6.78792', 'vk6.80365', 'vk6.80383', 'vk6.81783', 'vk6.87794', 'vk6.89153', 'vk6.89338']
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 O1O2O3U1U4U3O5O6O4U2U6U5
R3 orbit {'O1O2O3U1U4U3O5O6O4U2U6U5'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U1U5O4O6O5U3U2U6
Gauss code of K* O1O2O3U4U1U5O4O6O5U3U2U6
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 -1 2 1 0 0],[ 2 0 2 1 1 1 1],[ 1 -2 0 1 0 1 0],[-2 -1 -1 0 -2 -1 -1],[-1 -1 0 2 0 -1 0],[ 0 -1 -1 1 1 0 0],[ 0 -1 0 1 0 0 0]]
Primitive based matrix [[ 0 2 1 -1 -2],[-2 0 -2 -1 -1],[-1 2 0 0 -1],[ 1 1 0 0 -2],[ 2 1 1 2 0]]
If based matrix primitive False
Phi of primitive based matrix [-2,-1,1,2,2,1,1,0,1,2]
Phi over symmetry [-2,-1,1,2,-1,2,3,2,2,-1]
Phi of -K [-2,-1,1,2,-1,2,3,2,2,-1]
Phi of K* [-2,-1,1,2,-1,2,3,2,2,-1]
Phi of -K* [-2,-1,1,2,2,1,1,0,1,2]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 4z+9
Enhanced Jones-Krushkal polynomial 8w^4z-14w^3z+8w^3+10w^2z+w
Inner characteristic polynomial t^4+11t^2+9
Outer characteristic polynomial t^5+21t^3+45t
Flat arrow polynomial -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3
2-strand cable arrow polynomial -32*K1**4 - 768*K1**2*K2**2 + 768*K1**2*K2 - 32*K1**2*K3**2 - 1544*K1**2 + 320*K1*K2**3*K3 + 2560*K1*K2*K3 + 256*K1*K3*K4 + 64*K1*K4*K5 - 400*K2**4 - 800*K2**2*K3**2 - 16*K2**2*K4**2 + 144*K2**2*K4 - 1036*K2**2 + 528*K2*K3*K5 + 32*K2*K4*K6 - 1184*K3**2 - 172*K4**2 - 136*K5**2 - 12*K6**2 + 1458
Genus of based matrix 0
Fillings of based matrix [[{5, 6}, {2, 4}, {1, 3}], [{6}, {5}, {2, 4}, {1, 3}]]
If K is slice True
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