Tomographical aspects of L-convex polyominoes
Antonio Restivo, Giuseppa Castiglione, Andrea Frosini, Simone Rinaldi · Pure mathematics and applications · 2007
Our main purpose is to characterize the class of L-convex polyomi- noes introduced in (3) by means of their horizontal and vertical projections. The achieved results allow an answer to one of the most relevant questions in to- mography i.e. the uniqueness of discrete sets, with respect to their horizontal and vertical projections. In this paper, by giving a characterization of L-convex polyominoes, we investigate the connection between uniqueness property and unimodality of vectors of horizontal and vertical projections. In the last section we consider the continuum environment: we extend the definition of L-convex set, and we obtain some results analogous to those holding in the discrete case.