Tomographical aspects of L-convex polyominoes
نویسندگان
چکیده
Our main purpose is to characterize the class of L-convex polyominoes 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 tomography 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. Mathematics Subject Classifications (2000). 68Q25, 68W40
منابع مشابه
Two Subclasses of 2-convex Polyominoes: Properties for Reconstruction
A polyomino P is called 2-convex if for every two cells there exists a monotone path included in P with at most 2 changes of direction. This paper studies the tomographical aspects of two subclasses of 2-convex polyominoes called η2L and η′ 2L. In the first part, the uniqueness results of the two subclasses of HV convex polyominoes η and η′ are investigated using the switching components (that ...
متن کامل2L convex polyominoes: discrete tomographical aspects
This paper uses the theoretical material developed in a previous article by the authors in order to reconstruct a subclass of 2Lconvex polyominoes. The main idea is to control the shape of these polyominoes by combining 4 types of geometries. Some modifications are made in the reconstruction algorithm of Chrobak and Dürr for HV convex polyominoes in order to impose these geometries.
متن کاملReconstruction 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 ...
متن کاملReconstructing convex permutominoes
This paper studies the tomographical aspects of a new class of polyominoes, called permutominoes, which are defined by means of a pair of permutations. We inspect the classical problems of uniqueness and reconstruction on these objects, and in particular, using some combinatorial properties of their horizontal and vertical projections, we furnish a polynomial time reconstruction algorithm.
متن کاملTiling the Plane with Permutations
A permutomino is a polyomino uniquely defined by a pair of permutations. Recently permutominoes, and in particular convex permutominoes have been studied by several authors concerning their analytical and bijective enumeration, tomographical reconstruction, and the algebraic characterization of the associated permutations [2, 3]. On the other side, Beauquier and Nivat [5] introduced and gave a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008