JPD-coloring of the monohedral tiling for the plane. (English) Zbl 1347.52017

Summary: We introduce a definition of coloring by using joint probability distribution “JPD-coloring” for the plane which is equipped by tiling \(\mathfrak{I}\). We investigate the JPD-coloring of the \(r\)-monohedral tiling for the plane by mutually congruent regular convex polygons which are equilateral triangles at \(r=3\) or squares at \(r=4\) or regular hexagons at \(r=6\). Moreover we present some computations for determining the corresponding probability values which are used to color in the three studied cases by MAPLE-Package.


52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
60D05 Geometric probability and stochastic geometry


Full Text: DOI


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