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LayeredGraphPlot[GeneralizedGridGraph[{10"Directed",10"Directed"}],AspectRatio1]
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What is this invariant under?
What is this invariant under?
Coordinates of points are {t,x} or {t,x1,x2}
Isometry group:
What matrices preserve the arrows here?
Undirected graph case
Undirected graph case
Positions are {x,y}
What matrices leave infinite plane invariant?
{{0,1},{1,0}}
What is ISO(2Z) ?
Rotations + translations
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Select[Partition[#,2]&/@Tuples[{-1,0,1},4],OrthogonalMatrixQ]
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{{1,0},{0,-1}}.{x,y}
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{x,-y}
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Select[Partition[#,2]&/@Tuples[{-2,-1,0,1,2},4],OrthogonalMatrixQ]
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Claim: for the 3-direction case, you have to use complex numbers in the coordinates in order to have a matrix representation
Claim: for the 3-direction case, you have to use complex numbers in the coordinates in order to have a matrix representation
In the general case:
In the general case:
{t,b,x}