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Flat knot 6.1819

Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,1,2,1,4,2,0,3,1,0,0,2,2,1,0]
Flat knots (up to 7 crossings) with same phi are :['6.1819']
Arrow polynomial of the knot is: 8*K1**3 - 8*K1**2 - 4*K1*K2 - 4*K1 + 4*K2 + 5
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.570', '6.808', '6.1005', '6.1045', '6.1134', '6.1538', '6.1819']
Outer characteristic polynomial of the knot is: t^7+27t^5+136t^3+13t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1819']
2-strand cable arrow polynomial of the knot is: -256*K1**4*K2**2 + 384*K1**4*K2 - 928*K1**4 + 128*K1**3*K2*K3 - 192*K1**3*K3 - 1792*K1**2*K2**4 + 4608*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 9216*K1**2*K2**2 - 320*K1**2*K2*K4 + 8080*K1**2*K2 - 32*K1**2*K3**2 - 5048*K1**2 + 2240*K1*K2**3*K3 - 2176*K1*K2**2*K3 - 320*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 6336*K1*K2*K3 + 288*K1*K3*K4 - 704*K2**6 + 448*K2**4*K4 - 3744*K2**4 - 736*K2**2*K3**2 - 48*K2**2*K4**2 + 2384*K2**2*K4 - 1568*K2**2 + 208*K2*K3*K5 - 1312*K3**2 - 272*K4**2 - 8*K5**2 + 3502
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1819']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.70413', 'vk6.70420', 'vk6.70437', 'vk6.70452', 'vk6.70539', 'vk6.70619', 'vk6.70779', 'vk6.70862', 'vk6.70878', 'vk6.70895', 'vk6.70908', 'vk6.71026', 'vk6.71136', 'vk6.71260', 'vk6.71841', 'vk6.72280', 'vk6.76677', 'vk6.77636', 'vk6.87973', 'vk6.89213']
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 O1O2O3U1U2O4U3O5O6U4U5U6
R3 orbit {'O1O2O3U1U2O4U3O5O6U4U5U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U5U6O4O5U1O6U2U3
Gauss code of K* O1O2O3U4U5U6O4O5U1O6U2U3
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 -2 0 1 -1 0 2],[ 2 0 1 2 1 0 0],[ 0 -1 0 1 1 0 0],[-1 -2 -1 0 1 1 1],[ 1 -1 -1 -1 0 1 2],[ 0 0 0 -1 -1 0 1],[-2 0 0 -1 -2 -1 0]]
Primitive based matrix [[ 0 2 1 0 0 -1 -2],[-2 0 -1 0 -1 -2 0],[-1 1 0 -1 1 1 -2],[ 0 0 1 0 0 1 -1],[ 0 1 -1 0 0 -1 0],[ 1 2 -1 -1 1 0 -1],[ 2 0 2 1 0 1 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-1,0,0,1,2,1,0,1,2,0,1,-1,-1,2,0,-1,1,1,0,1]
Phi over symmetry [-2,-1,0,0,1,2,0,1,2,1,4,2,0,3,1,0,0,2,2,1,0]
Phi of -K [-2,-1,0,0,1,2,0,1,2,1,4,2,0,3,1,0,0,2,2,1,0]
Phi of K* [-2,-1,0,0,1,2,0,1,2,1,4,2,0,3,1,0,0,2,2,1,0]
Phi of -K* [-2,-1,0,0,1,2,1,0,1,2,0,1,-1,-1,2,0,-1,1,1,0,1]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 5z^2+22z+25
Enhanced Jones-Krushkal polynomial -2w^4z^2+7w^3z^2-4w^3z+26w^2z+25w
Inner characteristic polynomial t^6+17t^4+26t^2+1
Outer characteristic polynomial t^7+27t^5+136t^3+13t
Flat arrow polynomial 8*K1**3 - 8*K1**2 - 4*K1*K2 - 4*K1 + 4*K2 + 5
2-strand cable arrow polynomial -256*K1**4*K2**2 + 384*K1**4*K2 - 928*K1**4 + 128*K1**3*K2*K3 - 192*K1**3*K3 - 1792*K1**2*K2**4 + 4608*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 9216*K1**2*K2**2 - 320*K1**2*K2*K4 + 8080*K1**2*K2 - 32*K1**2*K3**2 - 5048*K1**2 + 2240*K1*K2**3*K3 - 2176*K1*K2**2*K3 - 320*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 6336*K1*K2*K3 + 288*K1*K3*K4 - 704*K2**6 + 448*K2**4*K4 - 3744*K2**4 - 736*K2**2*K3**2 - 48*K2**2*K4**2 + 2384*K2**2*K4 - 1568*K2**2 + 208*K2*K3*K5 - 1312*K3**2 - 272*K4**2 - 8*K5**2 + 3502
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}]]
If K is slice True
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