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Flat knot 6.1607

Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,2,2,2,0,1,1,1,1,1,1,-1,0,0]
Flat knots (up to 7 crossings) with same phi are :['6.1607']
Arrow polynomial of the knot is: -14*K1**2 + 7*K2 + 8
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1470', '6.1607']
Outer characteristic polynomial of the knot is: t^7+28t^5+23t^3+4t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1607', '6.1714']
2-strand cable arrow polynomial of the knot is: -448*K1**6 - 320*K1**4*K2**2 + 1632*K1**4*K2 - 6416*K1**4 + 768*K1**3*K2*K3 - 992*K1**3*K3 - 6432*K1**2*K2**2 - 416*K1**2*K2*K4 + 13248*K1**2*K2 - 496*K1**2*K3**2 - 5788*K1**2 - 224*K1*K2**2*K3 + 7232*K1*K2*K3 + 568*K1*K3*K4 - 344*K2**4 + 512*K2**2*K4 - 5272*K2**2 - 1916*K3**2 - 246*K4**2 + 5348
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1607']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20023', 'vk6.20066', 'vk6.21293', 'vk6.21348', 'vk6.27074', 'vk6.27127', 'vk6.28777', 'vk6.28816', 'vk6.38471', 'vk6.38524', 'vk6.40658', 'vk6.40721', 'vk6.45355', 'vk6.45420', 'vk6.47122', 'vk6.47162', 'vk6.56822', 'vk6.56887', 'vk6.57954', 'vk6.58025', 'vk6.61340', 'vk6.61413', 'vk6.62514', 'vk6.62570', 'vk6.66542', 'vk6.66587', 'vk6.67329', 'vk6.67378', 'vk6.69188', 'vk6.69235', 'vk6.69937', 'vk6.69976']
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 O1O2O3U2O4U1U5O6U3O5U4U6
R3 orbit {'O1O2O3U2O4U1U5O6U3O5U4U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U5O6U1O4U6U3O5U2
Gauss code of K* O1O2U3O4U2O5O3U1U6U4O6U5
Gauss code of -K* O1O2U3O4U1O3O5U2O6U4U6U5
Diagrammatic symmetry type c
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 -1 1 1 0 1],[ 2 0 0 2 2 1 2],[ 1 0 0 1 1 0 1],[-1 -2 -1 0 0 -1 1],[-1 -2 -1 0 0 -1 0],[ 0 -1 0 1 1 0 1],[-1 -2 -1 -1 0 -1 0]]
Primitive based matrix [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 -1 -1 -2],[-1 -1 0 0 -1 -1 -2],[-1 0 0 0 -1 -1 -2],[ 0 1 1 1 0 0 -1],[ 1 1 1 1 0 0 0],[ 2 2 2 2 1 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-1,-1,-1,0,1,2,-1,0,1,1,2,0,1,1,2,1,1,2,0,1,0]
Phi over symmetry [-2,-1,0,1,1,1,0,1,2,2,2,0,1,1,1,1,1,1,-1,0,0]
Phi of -K [-2,-1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,-1,0,0]
Phi of K* [-1,-1,-1,0,1,2,-1,0,0,1,1,0,0,1,1,0,1,1,1,1,1]
Phi of -K* [-2,-1,0,1,1,1,0,1,2,2,2,0,1,1,1,1,1,1,-1,0,0]
Symmetry type of based matrix c
u-polynomial t^2-2t
Normalized Jones-Krushkal polynomial z^2+22z+41
Enhanced Jones-Krushkal polynomial w^3z^2+22w^2z+41w
Inner characteristic polynomial t^6+20t^4+10t^2+1
Outer characteristic polynomial t^7+28t^5+23t^3+4t
Flat arrow polynomial -14*K1**2 + 7*K2 + 8
2-strand cable arrow polynomial -448*K1**6 - 320*K1**4*K2**2 + 1632*K1**4*K2 - 6416*K1**4 + 768*K1**3*K2*K3 - 992*K1**3*K3 - 6432*K1**2*K2**2 - 416*K1**2*K2*K4 + 13248*K1**2*K2 - 496*K1**2*K3**2 - 5788*K1**2 - 224*K1*K2**2*K3 + 7232*K1*K2*K3 + 568*K1*K3*K4 - 344*K2**4 + 512*K2**2*K4 - 5272*K2**2 - 1916*K3**2 - 246*K4**2 + 5348
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {4, 5}, {2, 3}], [{4, 6}, {1, 5}, {2, 3}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}]]
If K is slice False
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