We study the combinatorial properties and the problem of generating exhaustively double
square tiles, ie polyominoes yielding two distinct periodic tilings by translated copies such …

It has been proved that, among the polyominoes that tile the plane by translation, the so-
called squares tile the plane in at most two distinct ways. In this paper, we focus on double …

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We consider the tilings by translation of a single polyomino or tile on the square grid Z2. It is
well-known that there are two regular tilings of the plane, namely, parallelogram and …

The Freeman chain code is a common and useful way for representing discrete paths by
means of words such that each letter encodes a step in a given direction. In the discrete …

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) …

We study words on the 2-letter alphabet T={L, R} coding simple paths in the discrete plane
Z× iZ. A recurrence formula allows to build paths that are simple and linked with a class of …

A plane tiling consisting of congruent copies of a shape is isohedral provided that for any
pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We give a …

An unknown planar discrete set of points A can be inspected by means of a probe P of
generic shape that moves around it, and reveals, for each position, the number of its …

In this paper we consider several types of equations on words, motivated by the attempt of
characterizing the class of polyominoes that tile the plane by translation in two distinct ways …