Reconstructing discrete bidimensional sets from their projections is involved in many different problems of computer-aided tomography, pattern recognition, image processing and data compression. In this paper, we examine the problem of reconstructing a discrete bidimensional set S satisfying some convexity conditions from its two orthogonal projections (H, v). We develop an algorithm that start...

We will introduce the gap number of a polyomino, and prove that in the case of the T tetromino, it is finite. In particular, we will show that any rectangle having both sides at least 12 can be tiled with T tetrominos and at most 20 1 × 1 monominos.

Let the R2 space be divided into unit squares where a polyomino is a finite, connected set of unit squares. In this paper, we give a necessary and sufficient condition on tessellating polyominos by observing an unexpected relation between such tessellations and systems of arithmetic progressions. © 2006 Elsevier B.V. All rights reserved.

The present note is devoted to establish some extremal results for the zeroth-order general Randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

Whilst Polyomino tiling theory has been extensively studied as a branch of research in mathematics, its application has been largely confined to multimedia, graphics and gaming domains. In this paper, we present a novel application of Tromino tiling theory, a class of Polyomino with three cells in the context of a reconfigurable floor cleaning robot, hTromo. The developed robot platform is able...

Abstract How many chess rooks or queens does it take to guard all squares of a given polyomino, the union square tiles from grid? This question is version art gallery problem in which guards can “see” whichever rook queen attacks. We show that $$\lfloor {\frac{n}{2}} \rfloor $$ ⌊n<mml...