Results 1 - 10 of 366

Generating Convex Polyominoes at Random

by Winfried Hochstättler , Martin Loebl , Christoph Moll , 1992
"... We give a new recursion formula for the number of convex polyominoes with fixed perimeter. From this we derive a bijection between an intervall of natural numbers and the polyominoes of given perimeter. This provides a possibility to generate such polyominoes at random in polynomial time. Our method ..."
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We give a new recursion formula for the number of convex polyominoes with fixed perimeter. From this we derive a bijection between an intervall of natural numbers and the polyominoes of given perimeter. This provides a possibility to generate such polyominoes at random in polynomial time. Our

The number of Z-convex polyominoes

by Enrica Duchi, Simone Rinaldi, Gilles Schaeffer , 2006
"... In this paper we consider a restricted class of polyominoes that we call Z-convex polyominoes. Z-convex polyominoes are polyominoes such that any two pairs of cells can be connected by a monotone path making at most two turns (like the letter Z). In particular they are convex polyominoes, but they ..."
Abstract - Cited by 4 (2 self) - Add to MetaCart
that the generating function P(t) of Z-convex polyominoes with respect to the semi-perimeter can be expressed as a simple rational function of t and the generating function of Catalan numbers, like the generating function of convex polyominoes.

On The Number Of Convex Polyominoes

by Ira M. Gessel , 1999
"... . Lin and Chang gave a generating function for the number of convex polyominoes with an m+1byn+ 1 minimal bounding rectangle. We show that their result implies that the number of such polyominoes is m+ n +mn m+ n # 2m +2n 2m # - 2(m + n) # m+ n - 1 m ## m+ n - 1 n # . Resum e. Lin ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
. Lin and Chang gave a generating function for the number of convex polyominoes with an m+1byn+ 1 minimal bounding rectangle. We show that their result implies that the number of such polyominoes is m+ n +mn m+ n # 2m +2n 2m # - 2(m + n) # m+ n - 1 m ## m+ n - 1 n # . Resum e

An Object Grammar for Column-Convex Polyominoes

by E. Duchi, S. Rinaldi - ANNALS OF COMBINATORICS , 2004
"... In this paper we propose an object grammar decomposition for the classes of column-convex, and directed column-convex polyominoes. As a consequence, we obtain the enumeration of such classes according to the semi-perimeter, thus giving a natural explanation of the fact that the generating functions ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
In this paper we propose an object grammar decomposition for the classes of column-convex, and directed column-convex polyominoes. As a consequence, we obtain the enumeration of such classes according to the semi-perimeter, thus giving a natural explanation of the fact that the generating

The Number of Convex Polyominoes and the Generating Function of Jacobi Polynomials

by Victor J. W. Guo, Jiang Zeng, J. Riordan , 2004
"... Abstract. Lin and Chang gave a generating function of convex polyominoes with an m + 1 by n + 1 minimal bounding rectangle. Gessel showed that their result implies that the number of such polyominoes is m + n + mn m + n ..."
Abstract - Cited by 3 (3 self) - Add to MetaCart
Abstract. Lin and Chang gave a generating function of convex polyominoes with an m + 1 by n + 1 minimal bounding rectangle. Gessel showed that their result implies that the number of such polyominoes is m + n + mn m + n

Asymptotic Analysis and Random Sampling of Digitally Convex Polyominoes

by O. Bodini, Ph. Duchon, A. Jacquot, L. Mutafchiev , 2013
"... Recent work of Brlek et al. gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convex polyominoes and use it to analyze their limit properties and build a uniform sampler. Experimentally, ..."
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Recent work of Brlek et al. gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convex polyominoes and use it to analyze their limit properties and build a uniform sampler. Experimentally

On the generation and enumeration of some classes of convex polyominoes

by A. Del Lungo, E. Duchi, A. Frosini, S. Rinaldi , 2004
"... ..."
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Abstract not found

Random generation of Q-convex sets

by Sara Brunetti A, Alain Daurat B
"... The problem of randomly generating Q-convex sets is considered. We present two generators. The first one uses the Q-convex hull of a set of random points in order to generate a Q-convex set included in the square [0, n) 2. This generator is very simple, but is not uniform and its performance is quad ..."
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The problem of randomly generating Q-convex sets is considered. We present two generators. The first one uses the Q-convex hull of a set of random points in order to generate a Q-convex set included in the square [0, n) 2. This generator is very simple, but is not uniform and its performance

Enumeration of convex polyominoes using the ECO method

by A. Del Lungo, E. Duchi, A. Frosini, S. Rinaldi - in Discrete Models for Complex Systems, DMCS’03 , Michel Morvan an Éric Rémila (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AB, 103 , 2003
"... ECO is a method for the enumeration of classes of combinatorial objects based on recursive constructions of such classes. In the first part of this paper we present a construction for the class of convex polyominoes based on the ECO method. Then we translate this construction into a succession rule. ..."
Abstract - Cited by 7 (3 self) - Add to MetaCart
. The final goal of the paper is to determine the generating function of convex polyominoes according to the semi-perimeter, and it is achieved by applying an idea introduced in [11].

Enumeration of Symmetry Classes of Convex Polyominoes on the Honeycomb Lattice

by Dominique Gouyou-Beauchamps, et al. , 2004
"... We enumerate the symmetry classes of convex polyominoes on the hexagonal (honeycomb) lattice. Here convexity is to be understood as convexity along the three main column directions. We deduce the generating series of free (i.e. up to reflection and rotation) and of asymmetric convex hexagonal polyom ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
We enumerate the symmetry classes of convex polyominoes on the hexagonal (honeycomb) lattice. Here convexity is to be understood as convexity along the three main column directions. We deduce the generating series of free (i.e. up to reflection and rotation) and of asymmetric convex hexagonal
Results 1 - 10 of 366