On the tiling by translation problem

DOI10.1016/j.dam.2008.05.026zbMath1156.05014OpenAlexW2134122221MaRDI QIDQ1003706

Srečko Brlek, Jean-Marc Fedou, Xavier Provençal

Publication date: 4 March 2009

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2008.05.026

zbMATH Keywords

plane tesselationlongest common extensionstiling polyominoes

Mathematics Subject Classification ID

Combinatorial aspects of tessellation and tiling problems (05B45) Polyominoes (05B50)

Related Items (18)

Lyndon + Christoffel = digitally convex ⋮ Unnamed Item ⋮ On the shape of permutomino tiles ⋮ Combinatorial properties of double square tiles ⋮ Proving a conjecture on prime double square tiles ⋮ A parallelogram tile fills the plane by translation in at most two distinct ways ⋮ Non-lattice-periodic tilings of \(\mathbb R^3\) by single polycubes ⋮ About thin arithmetic discrete planes ⋮ Two infinite families of polyominoes that tile the plane by translation in two distinct ways ⋮ A linear time and space algorithm for detecting path intersection in \(\mathbb Z^d\) ⋮ A generalization of the Fibonacci word fractal and the Fibonacci snowflake ⋮ Combinatorial View of Digital Convexity ⋮ Arithmetic Discrete Planes Are Quasicrystals ⋮ Christoffel and Fibonacci Tiles ⋮ A Linear Time and Space Algorithm for Detecting Path Intersection ⋮ On the Number of p4-Tilings by an n-Omino ⋮ Unnamed Item ⋮ Convex and Concave Vertices on a Simple Closed Curve in the Triangular Grid

Cites Work

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• On translating one polyomino to tile the plane
• Linear time algorithms for finding and representing all the tandem repeats in a string
• Salient and Reentrant Points of Discrete Sets
• Arbitrary versus periodic storage schemes and tessellations of the plane using one type of polyomino
• Algorithms on Strings, Trees and Sequences
• Euclidean Paths: A New Representation of Boundary of Discrete Regions
• An algorithm for deciding if a polyomino tiles the plane
• Developments in Language Theory
• PROPERTIES OF THE CONTOUR PATH OF DISCRETE SETS
• The undecidability of the domino problem
• Checker Boards and Polyominoes

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