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Flat knot 6.1347

Min(phi) over symmetries of the knot is: [-3,-1,-1,1,2,2,1,1,2,2,3,0,1,2,1,1,2,1,1,0,0]
Flat knots (up to 7 crossings) with same phi are :['6.1347']
Arrow polynomial of the knot is: 8*K1**3 - 6*K1*K2 - 3*K1 + K3 + 1
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.67', '6.535', '6.1347', '6.1348', '6.1368']
Outer characteristic polynomial of the knot is: t^7+52t^5+85t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1347']
2-strand cable arrow polynomial of the knot is: -1024*K1**2*K2**4 + 640*K1**2*K2**3 - 3200*K1**2*K2**2 + 1744*K1**2*K2 - 776*K1**2 + 896*K1*K2**3*K3 + 2288*K1*K2*K3 + 128*K1*K3*K4 - 832*K2**6 + 640*K2**4*K4 - 2144*K2**4 - 256*K2**2*K3**2 - 152*K2**2*K4**2 + 1496*K2**2*K4 + 410*K2**2 + 32*K2*K3*K5 + 24*K2*K4*K6 - 472*K3**2 - 284*K4**2 - 2*K6**2 + 842
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1347']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73999', 'vk6.74003', 'vk6.74525', 'vk6.74529', 'vk6.75997', 'vk6.76738', 'vk6.76745', 'vk6.78976', 'vk6.79527', 'vk6.79533', 'vk6.80971', 'vk6.80974', 'vk6.83030', 'vk6.83637', 'vk6.83963', 'vk6.85208', 'vk6.85212', 'vk6.85291', 'vk6.85293', 'vk6.86563', 'vk6.87480', 'vk6.89306', 'vk6.89308', 'vk6.89820']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is +.
The reverse -K is
The reversed 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 O1O2O3U1O4O5U6U2U3O6U4U5
R3 orbit {'O1O2O3U1O4O5U6U2U3O6U4U5'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U5O6U1U2U6O4O5U3
Gauss code of K* Same
Gauss code of -K* O1O2O3U4U5O6U1U2U6O4O5U3
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 1 1 3 -2],[ 2 0 1 2 2 2 0],[ 1 -1 0 1 1 2 0],[-1 -2 -1 0 0 1 -1],[-1 -2 -1 0 0 1 -1],[-3 -2 -2 -1 -1 0 -3],[ 2 0 0 1 1 3 0]]
Primitive based matrix [[ 0 3 1 1 -1 -2 -2],[-3 0 -1 -1 -2 -2 -3],[-1 1 0 0 -1 -2 -1],[-1 1 0 0 -1 -2 -1],[ 1 2 1 1 0 -1 0],[ 2 2 2 2 1 0 0],[ 2 3 1 1 0 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-3,-1,-1,1,2,2,1,1,2,2,3,0,1,2,1,1,2,1,1,0,0]
Phi over symmetry [-3,-1,-1,1,2,2,1,1,2,2,3,0,1,2,1,1,2,1,1,0,0]
Phi of -K [-2,-2,-1,1,1,3,0,0,1,1,3,1,2,2,2,1,1,2,0,1,1]
Phi of K* [-3,-1,-1,1,2,2,1,1,2,2,3,0,1,2,1,1,2,1,1,0,0]
Phi of -K* [-2,-2,-1,1,1,3,0,0,1,1,3,1,2,2,2,1,1,2,0,1,1]
Symmetry type of based matrix +
u-polynomial -t^3+2t^2-t
Normalized Jones-Krushkal polynomial z+3
Enhanced Jones-Krushkal polynomial -12w^3z+13w^2z+3w
Inner characteristic polynomial t^6+32t^4+47t^2
Outer characteristic polynomial t^7+52t^5+85t^3
Flat arrow polynomial 8*K1**3 - 6*K1*K2 - 3*K1 + K3 + 1
2-strand cable arrow polynomial -1024*K1**2*K2**4 + 640*K1**2*K2**3 - 3200*K1**2*K2**2 + 1744*K1**2*K2 - 776*K1**2 + 896*K1*K2**3*K3 + 2288*K1*K2*K3 + 128*K1*K3*K4 - 832*K2**6 + 640*K2**4*K4 - 2144*K2**4 - 256*K2**2*K3**2 - 152*K2**2*K4**2 + 1496*K2**2*K4 + 410*K2**2 + 32*K2*K3*K5 + 24*K2*K4*K6 - 472*K3**2 - 284*K4**2 - 2*K6**2 + 842
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{1, 6}, {5}, {2, 4}, {3}], [{1, 6}, {5}, {3, 4}, {2}], [{1, 6}, {5}, {4}, {2, 3}], [{1, 6}, {5}, {4}, {3}, {2}], [{3, 6}, {1, 5}, {2, 4}], [{4, 6}, {1, 5}, {2, 3}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {2, 4}, {1, 3}]]
If K is slice False
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