To get x coordinates, pick a slice and crush it... Then we get a pure x grid
To get x coordinates, pick a slice and crush it... Then we get a pure grid
x
Valid metric signatures:
What is the shape of the region of equal-distance points
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diamondCausalGraphPlot[layerCount_:9,{lineDensityHorizontal_:1,lineDensityVertical_:1},{tanHorizontal_:0.0,tanVertical_:0.0},transform_:(#&)]:=DirectedGraphFlatten[Table[{v[{i,j}]v[{i+1,j}],v[{i,j}]v[{i+1,j+1}]},{i,layerCount-1},{j,i}]],VertexCoordinatesCatenate[Table[v[{i,j}]transform[{2(#2-#1/2),#1}&@@{i,j}],{i,layerCount},{j,i}]],VertexSize.33,VertexStyleDirectiveDirectiveOpacity[.7],,EdgeFormDirectiveOpacity[0.4],,VertexShapeFunction"Rectangle",Epilog{If[lineDensityHorizontal≠0,Style[Table[Line[transform/@{{-100,k-100tanHorizontal},{100,k+100tanHorizontal}}],{k,-100.5,100.5,1/lineDensityHorizontal}],Red],{}],If[lineDensityVertical≠0,Style[Table[Line[transform/@{{k-100tanVertical,-100},{k+100tanVertical,100}}],{k,-100.5,100.5,1/lineDensityVertical}],Red],{}]}
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diamondCausalGraphPlot[6,{0,0},{}]
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trans[f_,n_:10]:=DirectedGraph[Flatten[Table[{v[{i,j}]v[{i+1,j}],v[{i,j}]v[{i+1,j+1}]},{i,n},{j,i}]],VertexCoordinatesCatenate[Table[v[{i,j}]({#2-#1/2,-#1}&@@f[{i,j}]),{i,n+1},{j,i}]],VertexLabelsAutomatic]
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IndexGraph[trans[Identity,7]]
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Locus of equidistant points is a double light
Locus of points in continuum case is a hyperbola that limits to a cone when the interval is 0
Two approaches: {1,-1,-1,-1} or {1,1,1,1} with i c t as time coordinate
Two approaches: {1,-1,-1,-1} or {1,1,1,1} with i c t as time coordinate
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SeedRandom[23424];SkewPoset[YoungTableauToPoset@RandomTableau[{9,8,7,6,5,4,3,2,1}]]
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SeedRandom[23424];SkewPoset@YoungTableauToPoset@RandomTableau[{9,8,7,6,5,4,3,2,1}]
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