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Flat knot 6.2071

Min(phi) over symmetries of the knot is: [-1,-1,-1,1,1,1,-1,0,1,1,2,-1,1,1,1,0,1,1,-1,0,-1]
Flat knots (up to 7 crossings) with same phi are :['6.2071']
Arrow polynomial of the knot is: 8*K1**3 - 4*K1**2 - 12*K1*K2 + 2*K2 + 4*K3 + 3
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.2071']
Outer characteristic polynomial of the knot is: t^7+21t^5+59t^3+15t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2066', '6.2071', '7.44708']
2-strand cable arrow polynomial of the knot is: 3456*K1**4*K2 - 6784*K1**4 + 1664*K1**3*K2*K3 - 512*K1**3*K3 - 256*K1**2*K2**4 + 896*K1**2*K2**3 + 256*K1**2*K2**2*K4 - 10496*K1**2*K2**2 - 896*K1**2*K2*K4 + 10912*K1**2*K2 - 1280*K1**2*K3**2 - 64*K1**2*K4**2 - 2752*K1**2 + 768*K1*K2**3*K3 - 3200*K1*K2**2*K3 - 1024*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 9440*K1*K2*K3 + 1920*K1*K3*K4 + 320*K1*K4*K5 - 64*K2**6 + 192*K2**4*K4 - 1168*K2**4 - 320*K2**3*K6 - 832*K2**2*K3**2 - 144*K2**2*K4**2 + 2720*K2**2*K4 - 4912*K2**2 + 1056*K2*K3*K5 + 384*K2*K4*K6 - 2176*K3**2 - 924*K4**2 - 288*K5**2 - 96*K6**2 + 4330
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2071']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13820', 'vk6.13826', 'vk6.13842', 'vk6.13849', 'vk6.14892', 'vk6.14901', 'vk6.14924', 'vk6.14930', 'vk6.34245', 'vk6.34247', 'vk6.53831', 'vk6.53848', 'vk6.54374', 'vk6.54387']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is a.
The fillings (up to the first 10) associated to the algebraic genus:
Or click here to check the fillings

invariant value
Gauss code O1O2U1U3O4O3U5U2O5O6U4U6
R3 orbit {'O1O2U1U3O4O3U5U2O5O6U4U6'}
R3 orbit length 1
Gauss code of -K Same
Gauss code of K* Same
Gauss code of -K* Same
Diagrammatic symmetry type a
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 1 1 -1 -1 1],[ 1 0 1 1 1 0 0],[-1 -1 0 -1 -1 -1 1],[-1 -1 1 0 -1 -2 0],[ 1 -1 1 1 0 1 1],[ 1 0 1 2 -1 0 1],[-1 0 -1 0 -1 -1 0]]
Primitive based matrix [[ 0 1 1 1 -1 -1 -1],[-1 0 1 0 -1 -1 -2],[-1 -1 0 1 -1 -1 -1],[-1 0 -1 0 0 -1 -1],[ 1 1 1 0 0 1 0],[ 1 1 1 1 -1 0 1],[ 1 2 1 1 0 -1 0]]
If based matrix primitive True
Phi of primitive based matrix [-1,-1,-1,1,1,1,-1,0,1,1,2,-1,1,1,1,0,1,1,-1,0,-1]
Phi over symmetry [-1,-1,-1,1,1,1,-1,0,1,1,2,-1,1,1,1,0,1,1,-1,0,-1]
Phi of -K [-1,-1,-1,1,1,1,-1,0,1,1,2,-1,1,1,1,0,1,1,-1,0,-1]
Phi of K* [-1,-1,-1,1,1,1,-1,0,1,1,2,-1,1,1,1,0,1,1,-1,0,-1]
Phi of -K* [-1,-1,-1,1,1,1,-1,0,1,1,2,-1,1,1,1,0,1,1,-1,0,-1]
Symmetry type of based matrix a
u-polynomial 0
Normalized Jones-Krushkal polynomial 8z^2+28z+25
Enhanced Jones-Krushkal polynomial 8w^3z^2+28w^2z+25w
Inner characteristic polynomial t^6+15t^4+39t^2+9
Outer characteristic polynomial t^7+21t^5+59t^3+15t
Flat arrow polynomial 8*K1**3 - 4*K1**2 - 12*K1*K2 + 2*K2 + 4*K3 + 3
2-strand cable arrow polynomial 3456*K1**4*K2 - 6784*K1**4 + 1664*K1**3*K2*K3 - 512*K1**3*K3 - 256*K1**2*K2**4 + 896*K1**2*K2**3 + 256*K1**2*K2**2*K4 - 10496*K1**2*K2**2 - 896*K1**2*K2*K4 + 10912*K1**2*K2 - 1280*K1**2*K3**2 - 64*K1**2*K4**2 - 2752*K1**2 + 768*K1*K2**3*K3 - 3200*K1*K2**2*K3 - 1024*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 9440*K1*K2*K3 + 1920*K1*K3*K4 + 320*K1*K4*K5 - 64*K2**6 + 192*K2**4*K4 - 1168*K2**4 - 320*K2**3*K6 - 832*K2**2*K3**2 - 144*K2**2*K4**2 + 2720*K2**2*K4 - 4912*K2**2 + 1056*K2*K3*K5 + 384*K2*K4*K6 - 2176*K3**2 - 924*K4**2 - 288*K5**2 - 96*K6**2 + 4330
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {3, 5}, {2, 4}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}]]
If K is slice True
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