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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
About Half Permutations
We present a bijective correspondence between the class $D_n$ of directed column-convex permutominoes of size $n$ and a set of permutations (called $dcc$-permutations) of length $n+ 1$, which we prove to be counted by $(n+1)!/2$. Expand
Binary Pictures with Excluded Patterns
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
Polygons Drawn from Permutations
We prove that for every permutation π there is at least one column-convex permutomino P such that π1P = π if and only if $\cal{F}\pi$ is satisfiable. Expand
The number of directed k-convex polyominoes
We present a new method to obtain the generating functions for directed convex polyominoes according to several different statistics including: width, height, size of last column/row and number of corners. Expand
3-dimensional polygons determined by permutations
In this paper we introduce the notion of d-dimensional permupolygons on Z, with d ≥ 2. 2−dimensional permupolygons, also called permutominides, where introduced by Incitti et al. [12]. By using anExpand
Enumeration of polyominoes defined by combinatorial constraints
After an introductory part, where some basic definitions are provided and some motivations for the investigation are presented, the thesis is divided into two chapters. The first chapter concernsExpand
The Identity Transform of a Permutation and its Applications
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