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Flat knot 6.1905

Min(phi) over symmetries of the knot is: [-2,-2,0,0,2,2,0,0,1,0,2,1,0,2,0,0,1,0,0,1,0]
Flat knots (up to 7 crossings) with same phi are :['6.1905']
Arrow polynomial of the knot is: -16*K1**4 + 8*K1**2*K2 + 8*K1**2 + 1
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.113', '6.132', '6.220', '6.933', '6.1250', '6.1905']
Outer characteristic polynomial of the knot is: t^7+28t^5+132t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1905']
2-strand cable arrow polynomial of the knot is: -768*K2**8 + 512*K2**6*K4 - 2304*K2**6 - 64*K2**4*K4**2 + 1536*K2**4*K4 - 128*K2**4 - 128*K2**2*K4**2 + 736*K2**2*K4 + 608*K2**2 - 64*K4**2 + 62
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1905']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.70391', 'vk6.70394', 'vk6.70399', 'vk6.70404', 'vk6.70410', 'vk6.70412', 'vk6.70625', 'vk6.70792', 'vk6.70871', 'vk6.71035', 'vk6.71149', 'vk6.71266', 'vk6.89197', 'vk6.90107']
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 O1O2O3U1U2U3O4O5O6U4U5U6
R3 orbit {'O1O2O3U1U2U3O4O5O6U4U5U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U5U6O4O5O6U1U2U3
Gauss code of K* O1O2O3U4U5U6O4O5O6U1U2U3
Gauss code of -K* Same
Diagrammatic symmetry type -
Flat genus of the diagram 2
If K is checkerboard colorable True
If K is almost classical False
Based matrix from Gauss code [[ 0 -2 0 2 -2 0 2],[ 2 0 1 2 0 0 0],[ 0 -1 0 1 0 0 0],[-2 -2 -1 0 0 0 0],[ 2 0 0 0 0 1 2],[ 0 0 0 0 -1 0 1],[-2 0 0 0 -2 -1 0]]
Primitive based matrix [[ 0 2 2 0 0 -2 -2],[-2 0 0 0 -1 0 -2],[-2 0 0 -1 0 -2 0],[ 0 0 1 0 0 -1 0],[ 0 1 0 0 0 0 -1],[ 2 0 2 1 0 0 0],[ 2 2 0 0 1 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-2,0,0,2,2,0,0,1,0,2,1,0,2,0,0,1,0,0,1,0]
Phi over symmetry [-2,-2,0,0,2,2,0,0,1,0,2,1,0,2,0,0,1,0,0,1,0]
Phi of -K [-2,-2,0,0,2,2,0,1,2,2,4,2,1,4,2,0,1,2,2,1,0]
Phi of K* [-2,-2,0,0,2,2,0,1,2,2,4,2,1,4,2,0,1,2,2,1,0]
Phi of -K* [-2,-2,0,0,2,2,0,0,1,0,2,1,0,2,0,0,1,0,0,1,0]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial z^2+2z+1
Enhanced Jones-Krushkal polynomial -8w^4z^2+9w^3z^2+2w^2z+1
Inner characteristic polynomial t^6+12t^4+36t^2
Outer characteristic polynomial t^7+28t^5+132t^3
Flat arrow polynomial -16*K1**4 + 8*K1**2*K2 + 8*K1**2 + 1
2-strand cable arrow polynomial -768*K2**8 + 512*K2**6*K4 - 2304*K2**6 - 64*K2**4*K4**2 + 1536*K2**4*K4 - 128*K2**4 - 128*K2**2*K4**2 + 736*K2**2*K4 + 608*K2**2 - 64*K4**2 + 62
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {5}, {1, 3}, {2}]]
If K is slice True
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