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Flat knot 6.1929

Min(phi) over symmetries of the knot is: [-2,-2,0,0,2,2,0,0,1,3,3,1,0,3,3,0,0,1,1,0,0]
Flat knots (up to 7 crossings) with same phi are :['6.1929']
Arrow polynomial of the knot is: 8*K1**2*K2 - 8*K1**2 - 4*K2**2 + 5
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.89', '6.1214', '6.1929']
Outer characteristic polynomial of the knot is: t^7+40t^5+76t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1929']
2-strand cable arrow polynomial of the knot is: -64*K2**4*K4**2 + 256*K2**4*K4 - 1088*K2**4 + 128*K2**2*K4**3 - 768*K2**2*K4**2 + 2208*K2**2*K4 - 1040*K2**2 + 448*K2*K4*K6 - 48*K4**4 - 784*K4**2 - 80*K6**2 + 830
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1929']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.72502', 'vk6.72509', 'vk6.72552', 'vk6.72558', 'vk6.72936', 'vk6.72949', 'vk6.72974', 'vk6.72980', 'vk6.77823', 'vk6.77830', 'vk6.77836', 'vk6.77852', 'vk6.87266', 'vk6.90144']
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 O1O2O3U1U4U3O5O4O6U5U2U6
R3 orbit {'O1O2O3U1U4U3O5O4O6U5U2U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U2U5O4O6O5U1U6U3
Gauss code of K* O1O2O3U4U2U5O4O6O5U1U6U3
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 0 -2 2],[ 2 0 2 1 1 0 1],[ 0 -2 0 1 0 -1 2],[-2 -1 -1 0 -2 -1 0],[ 0 -1 0 2 0 -2 1],[ 2 0 1 1 2 0 1],[-2 -1 -2 0 -1 -1 0]]
Primitive based matrix [[ 0 2 2 0 0 -2 -2],[-2 0 0 -1 -2 -1 -1],[-2 0 0 -2 -1 -1 -1],[ 0 1 2 0 0 -1 -2],[ 0 2 1 0 0 -2 -1],[ 2 1 1 1 2 0 0],[ 2 1 1 2 1 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-2,0,0,2,2,0,1,2,1,1,2,1,1,1,0,1,2,2,1,0]
Phi over symmetry [-2,-2,0,0,2,2,0,0,1,3,3,1,0,3,3,0,0,1,1,0,0]
Phi of -K [-2,-2,0,0,2,2,0,0,1,3,3,1,0,3,3,0,0,1,1,0,0]
Phi of K* [-2,-2,0,0,2,2,0,0,1,3,3,1,0,3,3,0,0,1,1,0,0]
Phi of -K* [-2,-2,0,0,2,2,0,1,2,1,1,2,1,1,1,0,1,2,2,1,0]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 7z^2+20z+13
Enhanced Jones-Krushkal polynomial 7w^3z^2+20w^2z+13
Inner characteristic polynomial t^6+24t^4+44t^2
Outer characteristic polynomial t^7+40t^5+76t^3
Flat arrow polynomial 8*K1**2*K2 - 8*K1**2 - 4*K2**2 + 5
2-strand cable arrow polynomial -64*K2**4*K4**2 + 256*K2**4*K4 - 1088*K2**4 + 128*K2**2*K4**3 - 768*K2**2*K4**2 + 2208*K2**2*K4 - 1040*K2**2 + 448*K2*K4*K6 - 48*K4**4 - 784*K4**2 - 80*K6**2 + 830
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{5, 6}, {2, 4}, {1, 3}]]
If K is slice True
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