The algorithmic beauty of plants
The algorithmic beauty of plants
Euclidean paths: a new representation of boundary of discrete regions
Graphical Models and Image Processing
Lindenmayer Systems: Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology
Mathematical Theory of L Systems
Mathematical Theory of L Systems
On the tiling by translation problem
Discrete Applied Mathematics
An optimal algorithm for detecting pseudo-squares
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Equations on palindromes and circular words
Theoretical Computer Science
About thin arithmetic discrete planes
Theoretical Computer Science
Two infinite families of polyominoes that tile the plane by translation in two distinct ways
Theoretical Computer Science
A parallelogram tile fills the plane by translation in at most two distinct ways
Discrete Applied Mathematics
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Among the polyominoes that tile the plane by translation, the so-called squares have been conjectured to tile the plane in at most two distinct ways (these are called double squares). In this paper, we study two families of tiles : one is directly linked to Christoffel words while the other stems from the Fibonacci sequence. We show that these polyominoes are double squares, revealing strong connections between discrete geometry and other areas by means of combinatorics on words.