منابع مشابه
Parallelogram Polyominoes and Corners
(Received) We give an equation satissed by the generating function for parallelogram polyominoes according to the area, the width and the number of left path corners. Next, we give an explicit formula for the generating function of these polyominoes according to the area, the width and the number of right and left paths corners.
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 کاملCounting k-Convex Polyominoes
We compute an asymptotic estimate of a lower bound of the number of k-convex polyominoes of semiperimeter p. This approximation can be written as μ(k)p4p where μ(k) is a rational fraction of k which up to μ(k) is the asymptotics of convex polyominoes. A polyomino is a connected set of unit square cells drawn in the plane Z × Z [7]. The size of a polyomino is the number of its cells. A central p...
متن کاملStrictly Convex Corners Scatter
We prove the absence of non-scattering energies for potentials in the plane having a corner of angle smaller than π. This extends the earlier result of Bl̊asten, Päivärinta and Sylvester who considered rectangular corners. In three dimensions, we prove a similar result for any potential with a circular conic corner whose opening angle is outside a countable subset of (0, π).
متن کاملTwo 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 ...
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ژورنال
عنوان ژورنال: Open Journal of Discrete Mathematics
سال: 2019
ISSN: 2161-7635,2161-7643
DOI: 10.4236/ojdm.2019.92005