Daniela Battaglino

TL;DR: In this article, the authors considered the problem of enumerating a subclass of convex parallelogram polyominoes, precisely the $k$-$\textit{convex paralle logarithm polyomines} and gave a recursive decomposition for the class of parallelograms, which turns out to be a rational function.

TL;DR: In this article, an analogue of permutation classes in the context of polyominoes is introduced, where the submatrix-avoidance constraint is used to define permutation and polyomial classes with excluded submatrices.

TL;DR: This thesis considers the problem of characterising and enumerating sets of polyominoes described in terms of some constraints, defined either by convexity or by pattern containment, and introduces the concept of pattern avoidance in the context of matrices, more precisely permutation matrices andpolyomino matrices.

TL;DR: The notion of pattern avoidance is used in order to recognize or describe families of polyominoes defined by means of geometrical constraints or combinatorial properties, so that to be able to describe more families ofpolyominoe known in the literature.