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Flat knot 6.2064

Min(phi) over symmetries of the knot is: [-1,-1,-1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0]
Flat knots (up to 7 crossings) with same phi are :['6.2064', '7.44685']
Arrow polynomial of the knot is: 16*K1**3 - 12*K1**2 - 12*K1*K2 - 6*K1 + 6*K2 + 2*K3 + 7
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.141', '6.846', '6.918', '6.941', '6.2064', '6.2066']
Outer characteristic polynomial of the knot is: t^7+9t^5+15t^3+7t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2064', '7.44685']
2-strand cable arrow polynomial of the knot is: -2048*K1**6 - 6144*K1**4*K2**2 + 7680*K1**4*K2 - 4896*K1**4 + 3840*K1**3*K2*K3 - 1280*K1**3*K3 - 5760*K1**2*K2**4 + 9216*K1**2*K2**3 + 1536*K1**2*K2**2*K4 - 13248*K1**2*K2**2 - 2304*K1**2*K2*K4 + 8160*K1**2*K2 - 96*K1**2*K3**2 - 672*K1**2 + 4416*K1*K2**3*K3 - 2880*K1*K2**2*K3 - 1344*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 6336*K1*K2*K3 + 240*K1*K3*K4 + 48*K1*K4*K5 - 1536*K2**6 + 1536*K2**4*K4 - 3216*K2**4 - 320*K2**3*K6 - 384*K2**2*K3**2 - 144*K2**2*K4**2 + 2256*K2**2*K4 - 204*K2**2 + 192*K2*K3*K5 + 48*K2*K4*K6 - 392*K3**2 - 132*K4**2 - 24*K5**2 - 4*K6**2 + 1714
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2064']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.1', 'vk6.4', 'vk6.12', 'vk6.1169', 'vk6.1185', 'vk6.1193', 'vk6.2344', 'vk6.2351', 'vk6.33525', 'vk6.53768']
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 O1O2U1U2O3O4U3U4O5O6U5U6
R3 orbit {'O1O2U1U2O3O4U3U4O5O6U5U6'}
R3 orbit length 1
Gauss code of -K O1O2U3U4O3O4U5U6O5O6U1U2
Gauss code of K* O1O2U3U4O3O4U5U6O5O6U1U2
Gauss code of -K* Same
Diagrammatic symmetry type -
Flat genus of the diagram 3
If K is checkerboard colorable False
If K is almost classical False
Based matrix from Gauss code [[ 0 -1 1 -1 1 -1 1],[ 1 0 1 0 0 0 0],[-1 -1 0 0 0 0 0],[ 1 0 0 0 1 0 0],[-1 0 0 -1 0 0 0],[ 1 0 0 0 0 0 1],[-1 0 0 0 0 -1 0]]
Primitive based matrix [[ 0 1 1 1 -1 -1 -1],[-1 0 0 0 0 0 -1],[-1 0 0 0 0 -1 0],[-1 0 0 0 -1 0 0],[ 1 0 0 1 0 0 0],[ 1 0 1 0 0 0 0],[ 1 1 0 0 0 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-1,-1,-1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0]
Phi over symmetry [-1,-1,-1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0]
Phi of -K [-1,-1,-1,1,1,1,0,0,1,2,2,0,2,1,2,2,2,1,0,0,0]
Phi of K* [-1,-1,-1,1,1,1,0,0,1,2,2,0,2,1,2,2,2,1,0,0,0]
Phi of -K* [-1,-1,-1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 7z^2+27z+27
Enhanced Jones-Krushkal polynomial 7w^3z^2+27w^2z+27w
Inner characteristic polynomial t^6+3t^4+3t^2+1
Outer characteristic polynomial t^7+9t^5+15t^3+7t
Flat arrow polynomial 16*K1**3 - 12*K1**2 - 12*K1*K2 - 6*K1 + 6*K2 + 2*K3 + 7
2-strand cable arrow polynomial -2048*K1**6 - 6144*K1**4*K2**2 + 7680*K1**4*K2 - 4896*K1**4 + 3840*K1**3*K2*K3 - 1280*K1**3*K3 - 5760*K1**2*K2**4 + 9216*K1**2*K2**3 + 1536*K1**2*K2**2*K4 - 13248*K1**2*K2**2 - 2304*K1**2*K2*K4 + 8160*K1**2*K2 - 96*K1**2*K3**2 - 672*K1**2 + 4416*K1*K2**3*K3 - 2880*K1*K2**2*K3 - 1344*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 6336*K1*K2*K3 + 240*K1*K3*K4 + 48*K1*K4*K5 - 1536*K2**6 + 1536*K2**4*K4 - 3216*K2**4 - 320*K2**3*K6 - 384*K2**2*K3**2 - 144*K2**2*K4**2 + 2256*K2**2*K4 - 204*K2**2 + 192*K2*K3*K5 + 48*K2*K4*K6 - 392*K3**2 - 132*K4**2 - 24*K5**2 - 4*K6**2 + 1714
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}], [{3, 6}, {4, 5}, {1, 2}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {3, 4}, {1, 2}]]
If K is slice True
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