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Flat knot 6.1227

Min(phi) over symmetries of the knot is: [-2,-2,1,1,1,1,-2,0,1,2,3,1,1,1,1,0,0,0,0,0,0]
Flat knots (up to 7 crossings) with same phi are :['6.1227']
Arrow polynomial of the knot is: -4*K1*K2 + 2*K1 + 2*K3 + 1
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.540', '6.925', '6.1021', '6.1117', '6.1120', '6.1135', '6.1227', '6.1230', '6.1260', '6.1682', '6.1685', '6.1922']
Outer characteristic polynomial of the knot is: t^7+34t^5+64t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1227']
2-strand cable arrow polynomial of the knot is: -464*K1**4 + 96*K1**3*K3*K4 - 128*K1**2*K2**2 + 640*K1**2*K2 - 208*K1**2*K3**2 - 400*K1**2*K4**2 - 1040*K1**2 + 736*K1*K2*K3 + 1144*K1*K3*K4 + 552*K1*K4*K5 - 48*K2**2*K4**2 + 392*K2**2*K4 - 900*K2**2 + 96*K2*K3*K5 + 32*K2*K4*K6 - 788*K3**2 - 820*K4**2 - 236*K5**2 - 4*K6**2 + 1346
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1227']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4705', 'vk6.5012', 'vk6.6209', 'vk6.6676', 'vk6.8200', 'vk6.8625', 'vk6.9576', 'vk6.9913', 'vk6.17408', 'vk6.20928', 'vk6.21088', 'vk6.22340', 'vk6.22516', 'vk6.23580', 'vk6.23919', 'vk6.28409', 'vk6.36189', 'vk6.40075', 'vk6.40338', 'vk6.42126', 'vk6.43406', 'vk6.46604', 'vk6.46800', 'vk6.48055', 'vk6.48739', 'vk6.49746', 'vk6.50747', 'vk6.51438', 'vk6.57744', 'vk6.58936', 'vk6.65302', 'vk6.69776']
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 O1O2O3O4U3U2U1O5O6U5U4U6
R3 orbit {'O1O2O3O4U3U2U1O5O6U5U4U6'}
R3 orbit length 1
Gauss code of -K O1O2O3O4U5U1U6O5O6U4U3U2
Gauss code of K* O1O2O3U4U5O4O6O5U3U2U1U6
Gauss code of -K* O1O2O3U1U3O4O5O6U2U6U5U4
Diagrammatic symmetry type c
Flat genus of the diagram 2
If K is checkerboard colorable False
If K is almost classical False
Based matrix from Gauss code [[ 0 -1 -1 -1 2 -1 2],[ 1 0 0 0 3 0 1],[ 1 0 0 0 2 0 1],[ 1 0 0 0 1 0 1],[-2 -3 -2 -1 0 0 2],[ 1 0 0 0 0 0 1],[-2 -1 -1 -1 -2 -1 0]]
Primitive based matrix [[ 0 2 2 -1 -1 -1 -1],[-2 0 2 0 -1 -2 -3],[-2 -2 0 -1 -1 -1 -1],[ 1 0 1 0 0 0 0],[ 1 1 1 0 0 0 0],[ 1 2 1 0 0 0 0],[ 1 3 1 0 0 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-2,1,1,1,1,-2,0,1,2,3,1,1,1,1,0,0,0,0,0,0]
Phi over symmetry [-2,-2,1,1,1,1,-2,0,1,2,3,1,1,1,1,0,0,0,0,0,0]
Phi of -K [-1,-1,-1,-1,2,2,0,0,0,0,2,0,0,1,2,0,2,2,3,2,-2]
Phi of K* [-2,-2,1,1,1,1,-2,2,2,2,2,0,1,2,3,0,0,0,0,0,0]
Phi of -K* [-1,-1,-1,-1,2,2,0,0,0,0,1,0,0,1,1,0,2,1,3,1,2]
Symmetry type of based matrix c
u-polynomial -2t^2+4t
Normalized Jones-Krushkal polynomial 3z+7
Enhanced Jones-Krushkal polynomial 8w^4z-16w^3z+11w^2z+7w
Inner characteristic polynomial t^6+22t^4+20t^2
Outer characteristic polynomial t^7+34t^5+64t^3
Flat arrow polynomial -4*K1*K2 + 2*K1 + 2*K3 + 1
2-strand cable arrow polynomial -464*K1**4 + 96*K1**3*K3*K4 - 128*K1**2*K2**2 + 640*K1**2*K2 - 208*K1**2*K3**2 - 400*K1**2*K4**2 - 1040*K1**2 + 736*K1*K2*K3 + 1144*K1*K3*K4 + 552*K1*K4*K5 - 48*K2**2*K4**2 + 392*K2**2*K4 - 900*K2**2 + 96*K2*K3*K5 + 32*K2*K4*K6 - 788*K3**2 - 820*K4**2 - 236*K5**2 - 4*K6**2 + 1346
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {1, 5}, {2, 3}], [{6}, {4, 5}, {1, 3}, {2}]]
If K is slice False
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