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Flat knot 6.2017

Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,-1,0,1,1,1,1,0,0,1,-1,0,1,1,0,-1]
Flat knots (up to 7 crossings) with same phi are :['6.2017', '6.2039']
Arrow polynomial of the knot is: -12*K1**2 + 6*K2 + 7
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.612', '6.1246', '6.1402', '6.1410', '6.1411', '6.1468', '6.1617', '6.1666', '6.1667', '6.1815', '6.1904', '6.1994', '6.1995', '6.1996', '6.2001', '6.2014', '6.2015', '6.2016', '6.2017', '6.2020', '6.2022']
Outer characteristic polynomial of the knot is: t^7+18t^5+39t^3+5t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2017']
2-strand cable arrow polynomial of the knot is: -128*K1**4*K2**2 + 1088*K1**4*K2 - 2496*K1**4 + 192*K1**3*K2*K3 - 128*K1**3*K3 + 1216*K1**2*K2**3 - 6848*K1**2*K2**2 - 192*K1**2*K2*K4 + 7296*K1**2*K2 - 128*K1**2*K3**2 - 3024*K1**2 - 896*K1*K2**2*K3 + 4592*K1*K2*K3 + 208*K1*K3*K4 - 1136*K2**4 + 896*K2**2*K4 - 2168*K2**2 - 752*K3**2 - 132*K4**2 + 2538
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2017']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13946', 'vk6.14040', 'vk6.15013', 'vk6.15133', 'vk6.17451', 'vk6.17473', 'vk6.23960', 'vk6.23993', 'vk6.33758', 'vk6.33832', 'vk6.34297', 'vk6.36261', 'vk6.43422', 'vk6.53894', 'vk6.53926', 'vk6.54438', 'vk6.55590', 'vk6.60078', 'vk6.60091', 'vk6.65309']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is -.
The reverse -K is
The 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 O1O2U3O4U2O5U4U6O3O6U1U5
R3 orbit {'O1O2U3O4U2O5U4U6O3O6U1U5'}
R3 orbit length 1
Gauss code of -K O1O2U3U2O4O5U4U6O3U1O6U5
Gauss code of K* O1O2U3U2O4O5U4U6O3U1O6U5
Gauss code of -K* Same
Diagrammatic symmetry type -
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 0 -1 0 1 1],[ 1 0 0 -1 1 1 2],[ 0 0 0 -1 1 0 1],[ 1 1 1 0 0 1 1],[ 0 -1 -1 0 0 1 0],[-1 -1 0 -1 -1 0 -1],[-1 -2 -1 -1 0 1 0]]
Primitive based matrix [[ 0 1 1 0 0 -1 -1],[-1 0 1 0 -1 -1 -2],[-1 -1 0 -1 0 -1 -1],[ 0 0 1 0 -1 0 -1],[ 0 1 0 1 0 -1 0],[ 1 1 1 0 1 0 1],[ 1 2 1 1 0 -1 0]]
If based matrix primitive True
Phi of primitive based matrix [-1,-1,0,0,1,1,-1,0,1,1,2,1,0,1,1,1,0,1,1,0,-1]
Phi over symmetry [-1,-1,0,0,1,1,-1,0,1,1,1,1,0,0,1,-1,0,1,1,0,-1]
Phi of -K [-1,-1,0,0,1,1,-1,0,1,1,1,1,0,0,1,-1,0,1,1,0,-1]
Phi of K* [-1,-1,0,0,1,1,-1,0,1,1,1,1,0,0,1,-1,0,1,1,0,-1]
Phi of -K* [-1,-1,0,0,1,1,-1,0,1,1,2,1,0,1,1,1,0,1,1,0,-1]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 3z^2+20z+29
Enhanced Jones-Krushkal polynomial 3w^3z^2+20w^2z+29w
Inner characteristic polynomial t^6+14t^4+25t^2+1
Outer characteristic polynomial t^7+18t^5+39t^3+5t
Flat arrow polynomial -12*K1**2 + 6*K2 + 7
2-strand cable arrow polynomial -128*K1**4*K2**2 + 1088*K1**4*K2 - 2496*K1**4 + 192*K1**3*K2*K3 - 128*K1**3*K3 + 1216*K1**2*K2**3 - 6848*K1**2*K2**2 - 192*K1**2*K2*K4 + 7296*K1**2*K2 - 128*K1**2*K3**2 - 3024*K1**2 - 896*K1*K2**2*K3 + 4592*K1*K2*K3 + 208*K1*K3*K4 - 1136*K2**4 + 896*K2**2*K4 - 2168*K2**2 - 752*K3**2 - 132*K4**2 + 2538
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {3, 5}, {2, 4}]]
If K is slice True
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