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Encoding Centered Polyominoes by Means of a Regular Language
TLDR
A convex polyomino is k-convex if every pair of its cells can be connected by a monotone path with at most k changes of direction. Expand
The number of $k$-parallelogram polyominoes
A convex polyomino is $k$-$\textit{convex}$ if every pair of its cells can be connected by means of a $\textit{monotone path}$, internal to the polyomino, and having at most $k$ changes of direction.Expand
Permutation classes and polyomino classes with excluded submatrices
TLDR
This article introduces an analogue of permutation classes in the context of polyominoes. Expand
Enumeration of polyominoes defined in terms of pattern avoidance or convexity constraints. (Énumération de polyominos définis en terme d'évitement de motif ou de contraintes de convexité)
TLDR
We consider the problem of characterising and enumerating sets of polyominoes described in terms of some constraints, defined either by convexity or by pattern containment. Expand
A decomposition theorem for homogeneous sets with respect to diamond probes
TLDR
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 elements as a magnifying glass. Expand
Binary Pictures with Excluded Patterns
TLDR
We use the notion of pattern avoidance in order to recognize or describe families of polyominoes defined by means of geometrical constraints or combinatorial properties. Expand
Planar Configurations Induced by Exact Polyominoes
TLDR
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 elements as a magnifying glass. Expand
The Identity Transform of a Permutation and its Applications
TLDR
We study the set Cn, a set of permutations of the elements of the cyclic group Zn, and provide a different algorithm for the proof of Hall's Theore m. Expand