Questions tagged [tiling]

Use this tag for questions about (not necessarily periodic) tilings of metric spaces, their combinatorial, topological and dynamical properties, as well as basic definitions and concepts.

745 questions

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1 answer

Tricoloring of vertices of m*n grid

Every vertex of the unit squares on an $m$ x $n$ grid is colored either blue, green or red, such that all vertices on the boundary are colored red, where $m,n>0$ A square is properly colored if and only if one pair of its adjacent vertices are…

tiling

asked Sep 16 '19 at 19:12

Kai

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1 answer

Domino fault line

Let $n\ge 6$ be an even number. An $n$ by $n$ square is tiled by $2$ by $1$ dominoes. They can be placed horizontally or vertically. Must there exist a fault-line, or a line cutting the rectangle without cutting any domino? I have no clue how to…

tiling

asked Sep 11 '19 at 22:16

Kai

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0 answers

Number of labelings of symmetric hexagonal tilings

I am searching for the Number of labelings of symmetric hexagonal tilings If the hexagon is of the form P(n,n,n) then the coefficients can be found here A217311 I am looking for the coefficients of P(4,2,4) After doing some research I found…

tiling

asked Mar 23 '17 at 14:40

ZaMoC

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1 answer

A new periodic tiling of the plane

It is known if we use two convex polygons with equal sides we can cover the plane periodically in few ways. One new way to cover the plane periodically is if we use rhombuses and octagons of equal integer sides. My question is Is it possible for…

tiling