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Flat knot 6.1189

Min(phi) over symmetries of the knot is: [-2,-2,0,0,2,2,0,-1,1,2,3,0,1,3,3,-1,2,0,2,1,0]
Flat knots (up to 7 crossings) with same phi are :['6.1189']
Arrow polynomial of the knot is: -8*K1**4 + 8*K1**2*K2 - 2*K2**2 + 3
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1189', '6.1910']
Outer characteristic polynomial of the knot is: t^7+44t^5+152t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1189']
2-strand cable arrow polynomial of the knot is: -128*K2**8 + 256*K2**6*K4 - 1728*K2**6 - 192*K2**4*K4**2 + 1952*K2**4*K4 - 2560*K2**4 + 64*K2**2*K4**3 - 992*K2**2*K4**2 + 2728*K2**2*K4 + 316*K2**2 + 344*K2*K4*K6 - 8*K4**4 - 728*K4**2 - 60*K6**2 + 734
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1189']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.70471', 'vk6.70488', 'vk6.70527', 'vk6.70603', 'vk6.70649', 'vk6.70677', 'vk6.70759', 'vk6.70844', 'vk6.70935', 'vk6.70964', 'vk6.71008', 'vk6.71114', 'vk6.71165', 'vk6.71182', 'vk6.71248', 'vk6.71304', 'vk6.72389', 'vk6.72406', 'vk6.72738', 'vk6.73051', 'vk6.73616', 'vk6.74393', 'vk6.74936', 'vk6.75399', 'vk6.76504', 'vk6.76694', 'vk6.77726', 'vk6.78366', 'vk6.79437', 'vk6.79954', 'vk6.87178', 'vk6.90136']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is c.
The reverse -K is
The mirror image 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 O1O2O3O4U2U1U4O5O6U3U5U6
R3 orbit {'O1O2O3O4U2U1U4O5O6U3U5U6'}
R3 orbit length 1
Gauss code of -K O1O2O3O4U5U6U2O5O6U1U4U3
Gauss code of K* O1O2O3U4U5O6O4O5U2U1U6U3
Gauss code of -K* O1O2O3U1U2O4O5O6U4U3U6U5
Diagrammatic symmetry type c
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 -2 0 2 0 2],[ 2 0 0 3 2 1 1],[ 2 0 0 2 1 1 1],[ 0 -3 -2 0 0 1 2],[-2 -2 -1 0 0 0 0],[ 0 -1 -1 -1 0 0 1],[-2 -1 -1 -2 0 -1 0]]
Primitive based matrix [[ 0 2 2 0 0 -2 -2],[-2 0 0 0 0 -1 -2],[-2 0 0 -1 -2 -1 -1],[ 0 0 1 0 -1 -1 -1],[ 0 0 2 1 0 -2 -3],[ 2 1 1 1 2 0 0],[ 2 2 1 1 3 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-2,0,0,2,2,0,0,0,1,2,1,2,1,1,1,1,1,2,3,0]
Phi over symmetry [-2,-2,0,0,2,2,0,-1,1,2,3,0,1,3,3,-1,2,0,2,1,0]
Phi of -K [-2,-2,0,0,2,2,0,-1,1,2,3,0,1,3,3,-1,2,0,2,1,0]
Phi of K* [-2,-2,0,0,2,2,0,0,1,3,3,2,2,2,3,1,-1,0,1,1,0]
Phi of -K* [-2,-2,0,0,2,2,0,1,2,1,1,1,3,1,2,-1,1,0,2,0,0]
Symmetry type of based matrix c
u-polynomial 0
Normalized Jones-Krushkal polynomial 5z^2+14z+9
Enhanced Jones-Krushkal polynomial -6w^4z^2+11w^3z^2+14w^2z+9
Inner characteristic polynomial t^6+28t^4+40t^2
Outer characteristic polynomial t^7+44t^5+152t^3
Flat arrow polynomial -8*K1**4 + 8*K1**2*K2 - 2*K2**2 + 3
2-strand cable arrow polynomial -128*K2**8 + 256*K2**6*K4 - 1728*K2**6 - 192*K2**4*K4**2 + 1952*K2**4*K4 - 2560*K2**4 + 64*K2**2*K4**3 - 992*K2**2*K4**2 + 2728*K2**2*K4 + 316*K2**2 + 344*K2*K4*K6 - 8*K4**4 - 728*K4**2 - 60*K6**2 + 734
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {5}, {2, 4}, {3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {5}, {1, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {4, 5}, {1, 3}, {2}]]
If K is slice False
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