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Flat knot 6.1924

Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,0,1,1,2,0,0,1,1,1,0,1,0,0,-1]
Flat knots (up to 7 crossings) with same phi are :['6.1924', '7.31403', '7.41194']
Arrow polynomial of the knot is: 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.206', '6.236', '6.575', '6.580', '6.613', '6.619', '6.810', '6.819', '6.831', '6.838', '6.957', '6.1018', '6.1028', '6.1046', '6.1073', '6.1279', '6.1507', '6.1532', '6.1556', '6.1639', '6.1688', '6.1924', '6.1931']
Outer characteristic polynomial of the knot is: t^7+52t^5+90t^3+5t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1924', '7.41194']
2-strand cable arrow polynomial of the knot is: -1024*K1**4*K2**2 + 1856*K1**4*K2 - 1728*K1**4 + 448*K1**3*K2*K3 - 192*K1**3*K3 - 1152*K1**2*K2**4 + 3072*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 7392*K1**2*K2**2 - 512*K1**2*K2*K4 + 4528*K1**2*K2 - 1232*K1**2 + 896*K1*K2**3*K3 - 1088*K1*K2**2*K3 - 192*K1*K2**2*K5 + 3984*K1*K2*K3 + 80*K1*K3*K4 - 192*K2**6 + 128*K2**4*K4 - 1840*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 1216*K2**2*K4 - 464*K2**2 + 32*K2*K3*K5 - 416*K3**2 - 100*K4**2 + 1266
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1924']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.308', 'vk6.344', 'vk6.695', 'vk6.741', 'vk6.1489', 'vk6.1941', 'vk6.1978', 'vk6.2451', 'vk6.2630', 'vk6.3105', 'vk6.18264', 'vk6.18599', 'vk6.24748', 'vk6.25154', 'vk6.36879', 'vk6.37339', 'vk6.44099', 'vk6.56059', 'vk6.60614', 'vk6.65730']
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 O1O2O3U1U4U5O4O5O6U2U3U6
R3 orbit {'O1O2O3U1U4U5O4O5O6U2U3U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U2U3U4O5O6O4U1U5U6
Gauss code of K* O1O2O3U2U3U4O5O6O4U1U5U6
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 -1 1 -1 1 2],[ 2 0 1 2 2 2 2],[ 1 -1 0 1 0 2 2],[-1 -2 -1 0 -2 0 1],[ 1 -2 0 2 0 1 2],[-1 -2 -2 0 -1 0 2],[-2 -2 -2 -1 -2 -2 0]]
Primitive based matrix [[ 0 2 1 1 -1 -1 -2],[-2 0 -1 -2 -2 -2 -2],[-1 1 0 0 -1 -2 -2],[-1 2 0 0 -2 -1 -2],[ 1 2 1 2 0 0 -1],[ 1 2 2 1 0 0 -2],[ 2 2 2 2 1 2 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-1,-1,1,1,2,1,2,2,2,2,0,1,2,2,2,1,2,0,1,2]
Phi over symmetry [-2,-1,-1,1,1,2,-1,0,1,1,2,0,0,1,1,1,0,1,0,0,-1]
Phi of -K [-2,-1,-1,1,1,2,-1,0,1,1,2,0,0,1,1,1,0,1,0,0,-1]
Phi of K* [-2,-1,-1,1,1,2,-1,0,1,1,2,0,0,1,1,1,0,1,0,0,-1]
Phi of -K* [-2,-1,-1,1,1,2,1,2,2,2,2,0,1,2,2,2,1,2,0,1,2]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 7z^2+24z+21
Enhanced Jones-Krushkal polynomial 7w^3z^2+24w^2z+21w
Inner characteristic polynomial t^6+40t^4+64t^2+1
Outer characteristic polynomial t^7+52t^5+90t^3+5t
Flat arrow polynomial 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3
2-strand cable arrow polynomial -1024*K1**4*K2**2 + 1856*K1**4*K2 - 1728*K1**4 + 448*K1**3*K2*K3 - 192*K1**3*K3 - 1152*K1**2*K2**4 + 3072*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 7392*K1**2*K2**2 - 512*K1**2*K2*K4 + 4528*K1**2*K2 - 1232*K1**2 + 896*K1*K2**3*K3 - 1088*K1*K2**2*K3 - 192*K1*K2**2*K5 + 3984*K1*K2*K3 + 80*K1*K3*K4 - 192*K2**6 + 128*K2**4*K4 - 1840*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 1216*K2**2*K4 - 464*K2**2 + 32*K2*K3*K5 - 416*K3**2 - 100*K4**2 + 1266
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {4, 5}, {2, 3}]]
If K is slice True
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