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Flat knot 6.1130

Min(phi) over symmetries of the knot is: [-2,0,0,2,0,1,2,0,1,2]
Flat knots (up to 7 crossings) with same phi are :['6.1130']
Arrow polynomial of the knot is: -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.235', '6.379', '6.411', '6.547', '6.811', '6.818', '6.823', '6.897', '6.898', '6.1008', '6.1053', '6.1109', '6.1110', '6.1130', '6.1222', '6.1239', '6.1303', '6.1307', '6.1342', '6.1491', '6.1495', '6.1496', '6.1519', '6.1592', '6.1593', '6.1642', '6.1652', '6.1653', '6.1671', '6.1673', '6.1717']
Outer characteristic polynomial of the knot is: t^5+18t^3+9t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1130']
2-strand cable arrow polynomial of the knot is: -896*K1**6 + 1600*K1**4*K2 - 5792*K1**4 - 832*K1**3*K3 - 2816*K1**2*K2**2 - 704*K1**2*K2*K4 + 8720*K1**2*K2 - 1664*K1**2*K3**2 - 256*K1**2*K3*K5 - 448*K1**2*K4**2 - 32*K1**2*K5**2 - 4432*K1**2 - 256*K1*K2**2*K3 - 64*K1*K2*K3*K4 + 6464*K1*K2*K3 + 3536*K1*K3*K4 + 880*K1*K4*K5 + 80*K1*K5*K6 - 128*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 848*K2**2*K4 - 4428*K2**2 + 336*K2*K3*K5 + 32*K2*K4*K6 - 2912*K3**2 - 1576*K4**2 - 416*K5**2 - 44*K6**2 + 5310
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1130']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4784', 'vk6.5119', 'vk6.6350', 'vk6.6781', 'vk6.8311', 'vk6.8758', 'vk6.9685', 'vk6.9994', 'vk6.21003', 'vk6.22427', 'vk6.28455', 'vk6.40231', 'vk6.42162', 'vk6.46729', 'vk6.48817', 'vk6.49039', 'vk6.49859', 'vk6.51515', 'vk6.58966', 'vk6.69804']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is r.
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 O1O2O3O4U5U3O5U1U4O6U2U6
R3 orbit {'O1O2O3O4U5U3O5U1U4O6U2U6'}
R3 orbit length 1
Gauss code of -K Same
Gauss code of K* O1O2U1O3O4U5O6O5U3U6U2U4
Gauss code of -K* O1O2U1O3O4U5O6O5U3U6U2U4
Diagrammatic symmetry type r
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 0 0 2 -1 1],[ 2 0 2 1 2 1 1],[ 0 -2 0 0 1 -1 1],[ 0 -1 0 0 0 0 0],[-2 -2 -1 0 0 -2 0],[ 1 -1 1 0 2 0 1],[-1 -1 -1 0 0 -1 0]]
Primitive based matrix [[ 0 2 0 0 -2],[-2 0 0 -1 -2],[ 0 0 0 0 -1],[ 0 1 0 0 -2],[ 2 2 1 2 0]]
If based matrix primitive False
Phi of primitive based matrix [-2,0,0,2,0,1,2,0,1,2]
Phi over symmetry [-2,0,0,2,0,1,2,0,1,2]
Phi of -K [-2,0,0,2,0,1,2,0,1,2]
Phi of K* [-2,0,0,2,1,2,2,0,0,1]
Phi of -K* [-2,0,0,2,1,2,2,0,0,1]
Symmetry type of based matrix r
u-polynomial 0
Normalized Jones-Krushkal polynomial 21z+43
Enhanced Jones-Krushkal polynomial 21w^2z+43w
Inner characteristic polynomial t^4+10t^2+1
Outer characteristic polynomial t^5+18t^3+9t
Flat arrow polynomial -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5
2-strand cable arrow polynomial -896*K1**6 + 1600*K1**4*K2 - 5792*K1**4 - 832*K1**3*K3 - 2816*K1**2*K2**2 - 704*K1**2*K2*K4 + 8720*K1**2*K2 - 1664*K1**2*K3**2 - 256*K1**2*K3*K5 - 448*K1**2*K4**2 - 32*K1**2*K5**2 - 4432*K1**2 - 256*K1*K2**2*K3 - 64*K1*K2*K3*K4 + 6464*K1*K2*K3 + 3536*K1*K3*K4 + 880*K1*K4*K5 + 80*K1*K5*K6 - 128*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 848*K2**2*K4 - 4428*K2**2 + 336*K2*K3*K5 + 32*K2*K4*K6 - 2912*K3**2 - 1576*K4**2 - 416*K5**2 - 44*K6**2 + 5310
Genus of based matrix 1
Fillings of based matrix [[{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}]]
If K is slice False
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