Two Subclasses of 2-convex Polyominoes: Properties for Reconstruction

Some properties and results for certain subclasses of starlike and convex functions

In the present paper, we introduce and investigate some properties of two subclasses $ Lambda_{n}( lambda , beta ) $ and $ Lambda_{n}^{+}( lambda , beta ) $;  meromorphic and starlike  functions of order $ beta $. In particular, several inclusion relations, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes.

The Reconstruction of Polyominoes from Approximately Orthogonal Projections

The reconstruction of discrete two-dimensional pictures from their projection is one of the central problems in the areas of medical diagnostics, computer-aided tomography, pattern recognition, image processing, and data compression. In this note, we determine the computational complexity of the problem of reconstruction of polyominoes from their approximately orthogonal projections. We will pr...

Reconstruction of 2-convex polyominoes

There are many notions of discrete convexity of polyominoes (namely hvconvex [1], Q-convex [2], L-convex polyominoes [5]) and each one has been deeply studied. One natural notion of convexity on the discrete plane leads to the definition of the class of hv-convex polyominoes, that is polyominoes with consecutive cells in rows and columns. In [1] and [6], it has been shown how to reconstruct in ...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

ar X iv : 0 71 1 . 05 82 v 1 [ m at h . C O ] 5 N ov 2 00 7 PERMUTATIONS DEFINING CONVEX PERMUTOMINOES

A permutomino of size n is a polyomino determined by particular pairs (π1, π2) of permutations of size n, such that π1(i) 6= π2(i), for 1 ≤ i ≤ n. Here we determine the combinatorial properties and, in particular, the characterization for the permutations defining convex permutominoes. Using such a characterization, these permutations can be uniquely represented in terms of the so called square...