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

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

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

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

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

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 an… Expand

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 concerns… Expand

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