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Flat knot 6.2079

Min(phi) over symmetries of the knot is: [-1,0,0,0,0,1,0,0,0,0,2,-1,-1,0,0,0,0,0,1,0,0]
Flat knots (up to 7 crossings) with same phi are :['6.2079', '7.46225']
Arrow polynomial of the knot is: -16*K1**2 + 8*K2 + 9
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1244', '6.1401', '6.2079', '6.2084']
Outer characteristic polynomial of the knot is: t^7+13t^5+11t^3+2t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2079']
2-strand cable arrow polynomial of the knot is: -1024*K1**6 - 384*K1**4*K2**2 + 2304*K1**4*K2 - 8704*K1**4 + 640*K1**3*K2*K3 - 576*K1**3*K3 - 4704*K1**2*K2**2 - 64*K1**2*K2*K4 + 12000*K1**2*K2 - 320*K1**2*K3**2 - 2384*K1**2 + 4048*K1*K2*K3 + 96*K1*K3*K4 - 256*K2**4 + 256*K2**2*K4 - 3848*K2**2 - 928*K3**2 - 72*K4**2 + 3918
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2079']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4789', 'vk6.5126', 'vk6.6351', 'vk6.6784', 'vk6.8308', 'vk6.8757', 'vk6.9678', 'vk6.9989', 'vk6.21010', 'vk6.22432', 'vk6.28465', 'vk6.40238', 'vk6.42166', 'vk6.46740', 'vk6.48818', 'vk6.49046', 'vk6.49862', 'vk6.51514', 'vk6.58956', 'vk6.69800']
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 O1O2U1U3O4O5U6U5O3O6U2U4
R3 orbit {'O1O2U1U3O4O5U6U5O3O6U2U4'}
R3 orbit length 1
Gauss code of -K O1O2U3U1O3O4U2U5O6O5U4U6
Gauss code of K* O1O2U3U1O3O4U2U5O6O5U4U6
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 -1 0 0 0 1 0],[ 1 0 1 1 1 0 1],[ 0 -1 0 -1 0 1 0],[ 0 -1 1 0 1 1 0],[ 0 -1 0 -1 0 1 -1],[-1 0 -1 -1 -1 0 -1],[ 0 -1 0 0 1 1 0]]
Primitive based matrix [[ 0 1 0 0 0 0 -1],[-1 0 -1 -1 -1 -1 0],[ 0 1 0 1 1 0 -1],[ 0 1 -1 0 0 0 -1],[ 0 1 -1 0 0 -1 -1],[ 0 1 0 0 1 0 -1],[ 1 0 1 1 1 1 0]]
If based matrix primitive True
Phi of primitive based matrix [-1,0,0,0,0,1,1,1,1,1,0,-1,-1,0,1,0,0,1,1,1,1]
Phi over symmetry [-1,0,0,0,0,1,0,0,0,0,2,-1,-1,0,0,0,0,0,1,0,0]
Phi of -K [-1,0,0,0,0,1,0,0,0,0,2,-1,-1,0,0,0,0,0,1,0,0]
Phi of K* [-1,0,0,0,0,1,0,0,0,0,2,-1,-1,0,0,0,0,0,1,0,0]
Phi of -K* [-1,0,0,0,0,1,1,1,1,1,0,-1,-1,0,1,0,0,1,1,1,1]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 21z+43
Enhanced Jones-Krushkal polynomial 21w^2z+43w
Inner characteristic polynomial t^6+11t^4+5t^2
Outer characteristic polynomial t^7+13t^5+11t^3+2t
Flat arrow polynomial -16*K1**2 + 8*K2 + 9
2-strand cable arrow polynomial -1024*K1**6 - 384*K1**4*K2**2 + 2304*K1**4*K2 - 8704*K1**4 + 640*K1**3*K2*K3 - 576*K1**3*K3 - 4704*K1**2*K2**2 - 64*K1**2*K2*K4 + 12000*K1**2*K2 - 320*K1**2*K3**2 - 2384*K1**2 + 4048*K1*K2*K3 + 96*K1*K3*K4 - 256*K2**4 + 256*K2**2*K4 - 3848*K2**2 - 928*K3**2 - 72*K4**2 + 3918
Genus of based matrix 0
Fillings of based matrix [[{2, 6}, {1, 5}, {3, 4}]]
If K is slice True
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