# A Note on Tiling with Integer-Sided Rectangles

@article{Kenyon1996ANO, title={A Note on Tiling with Integer-Sided Rectangles}, author={Richard W. Kenyon}, journal={J. Comb. Theory, Ser. A}, year={1996}, volume={74}, pages={321-332} }

We show how to determine if a given rectilinear polygon can be tiled with rectangles, each having an integer side.

## 20 Citations

### Minimizing the Number of Tiles in a Tiled Rectangle

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In this paper, we prove that if a finite number of rectangles, every of which has at least one integer side, perfectly tile a big rectangle then there exists a strategy which reduces the number of…

### How to Tile by Dominoes the Boundary of a Polycube

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It is proved that the boundary of a polycube has always a tiling by foldable dominoes and the adjacency graph of the unit squares in the Boundary of a spherical poly cube has a Hamiltonian cycle.

### Tiling a Polygon with Two Kinds of Rectangles

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A quadratic time algorithm is given which, given a polygon F as input, produces a tiling of F with translated copies of the authors' rectangles (or indicates that there is no tiling), and it is proved that any pair oftilings can be linked by a sequence of local transformations of tilings, called flips.

### Optimal Partial Tiling of Manhattan Polyominoes

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This work has worked on a special case, the tiling of Manhattan polyominoes with dominoes, for which it gives an algorithm linear in the number of columns, borrowed from traditional graph optimisation problems.

### Group Theory and Tiling Problems

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Tiling subsets of the plane by polygonal shapes or more generally of subsets of higher-dimensional spaces by polyhedra is intimately connected with group theory. The factorization theory of groups…

### Ribbon tilings and multidimensional height functions

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We fix n and say a square in the two-dimensional grid indexed by (x, y) has color c if x + y ≡ c (mod n). A ribbon tile of order n is a connected polyomino containing exactly one square of each…

### Ribbon Tile Invariants from the Signed Area

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Here is a complete proof of the conjecture, which works by associating ribbon tiles with certain polygons in the complex plane, and deriving invariants from the signed area of these polygons.

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