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Flat knot 5.11

Min(phi) over symmetries of the knot is: [-4,0,1,1,2,2,1,4,3,0,1,1,0,0,1]
Flat knots (up to 7 crossings) with same phi are :['5.11']
Arrow polynomial of the knot is: -4*K1**2*K2 + 8*K1**2 + 2*K1*K3 - 3*K2 - 2
Flat knots (up to 7 crossings) with same arrow polynomial are :['5.11', '7.3533', '7.6056', '7.7042', '7.7816', '7.8225', '7.15945', '7.16006', '7.31357', '7.31361']
Outer characteristic polynomial of the knot is: t^6+55t^4+27t^2
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.11']
2-strand cable arrow polynomial of the knot is: -448*K1**4 - 608*K1**2*K2**2 + 944*K1**2*K2 - 520*K1**2 + 192*K1*K2**3*K3 + 784*K1*K2*K3 + 80*K1*K3*K4 - 32*K2**4*K4**2 + 96*K2**4*K4 - 304*K2**4 + 32*K2**3*K4*K6 - 192*K2**2*K3**2 - 96*K2**2*K4**2 + 232*K2**2*K4 - 8*K2**2*K6**2 - 436*K2**2 + 80*K2*K3*K5 + 32*K2*K4*K6 - 296*K3**2 - 118*K4**2 - 16*K5**2 - 4*K6**2 + 604
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.11']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.626', 'vk5.630', 'vk5.766', 'vk5.769', 'vk5.1129', 'vk5.1281', 'vk5.1287', 'vk5.1634', 'vk5.1750', 'vk5.1757', 'vk5.1921', 'vk5.1925']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is +.
The reverse -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 O1O2O3O4O5U1U5U3U4U2
R3 orbit {'O1O2O3O4O5U1U5U3U4U2'}
R3 orbit length 1
Gauss code of -K O1O2O3O4O5U4U2U3U1U5
Gauss code of K* Same
Gauss code of -K* O1O2O3O4O5U4U2U3U1U5
Diagrammatic symmetry type +
Flat genus of the diagram 2
If K is checkerboard colorable False
If K is almost classical False
Based matrix from Gauss code [[ 0 -4 1 0 2 1],[ 4 0 4 2 3 1],[-1 -4 0 -1 1 0],[ 0 -2 1 0 1 0],[-2 -3 -1 -1 0 0],[-1 -1 0 0 0 0]]
Primitive based matrix [[ 0 2 1 1 0 -4],[-2 0 0 -1 -1 -3],[-1 0 0 0 0 -1],[-1 1 0 0 -1 -4],[ 0 1 0 1 0 -2],[ 4 3 1 4 2 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-1,-1,0,4,0,1,1,3,0,0,1,1,4,2]
Phi over symmetry [-4,0,1,1,2,2,1,4,3,0,1,1,0,0,1]
Phi of -K [-4,0,1,1,2,2,1,4,3,0,1,1,0,0,1]
Phi of K* [-2,-1,-1,0,4,0,1,1,3,0,0,1,1,4,2]
Phi of -K* [-4,0,1,1,2,2,1,4,3,0,1,1,0,0,1]
Symmetry type of based matrix +
u-polynomial t^4-t^2-2t
Normalized Jones-Krushkal polynomial -7z-13
Enhanced Jones-Krushkal polynomial 2w^3z-9w^2z-13w
Inner characteristic polynomial t^5+33t^3+4t
Outer characteristic polynomial t^6+55t^4+27t^2
Flat arrow polynomial -4*K1**2*K2 + 8*K1**2 + 2*K1*K3 - 3*K2 - 2
2-strand cable arrow polynomial -448*K1**4 - 608*K1**2*K2**2 + 944*K1**2*K2 - 520*K1**2 + 192*K1*K2**3*K3 + 784*K1*K2*K3 + 80*K1*K3*K4 - 32*K2**4*K4**2 + 96*K2**4*K4 - 304*K2**4 + 32*K2**3*K4*K6 - 192*K2**2*K3**2 - 96*K2**2*K4**2 + 232*K2**2*K4 - 8*K2**2*K6**2 - 436*K2**2 + 80*K2*K3*K5 + 32*K2*K4*K6 - 296*K3**2 - 118*K4**2 - 16*K5**2 - 4*K6**2 + 604
Genus of based matrix 1
Fillings of based matrix [[{1, 5}, {2, 4}, {3}], [{2, 5}, {1, 4}, {3}], [{2, 5}, {3, 4}, {1}], [{2, 5}, {4}, {1, 3}], [{2, 5}, {4}, {3}, {1}], [{4, 5}, {3}, {1, 2}]]
If K is slice False
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