Discrete geometry redefines notions borrowed from Euclidean geometry creating a need for
new algorithmical tools. The notion of convexity does not translate trivially, and detecting if a …

In this paper we introduce a family of infinite words that generalize the Fibonacci word and
we study their combinatorial properties. We associate with this family of words a family of …

We consider paths in the 2D square grid, composed of grid edges, given as a sequence of
moves in the four cardinal compass directions, without U-turns, but possibly passing several …

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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In [2], while studying a relevant class of polyominoes that tile the plane by translation, ie,
double square polyominoes, the authors found that their boundary words, encoded by the …

In 2013, while studying a relevant class of polyominoes that tile the plane by translation, ie,
double square polyominoes, Blondin Massé et al. found that their boundary words, encoded …

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 …