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366
Generating Convex Polyominoes at Random
, 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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Cited by 5 (0 self)
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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 Zconvex polyominoes
, 2006
"... In this paper we consider a restricted class of polyominoes that we call Zconvex polyominoes. Zconvex 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 ..."
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Cited by 4 (2 self)
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that the generating function P(t) of Zconvex polyominoes with respect to the semiperimeter 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
, 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 ..."
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Cited by 8 (0 self)
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. 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 ColumnConvex Polyominoes
 ANNALS OF COMBINATORICS
, 2004
"... In this paper we propose an object grammar decomposition for the classes of columnconvex, and directed columnconvex polyominoes. As a consequence, we obtain the enumeration of such classes according to the semiperimeter, thus giving a natural explanation of the fact that the generating functions ..."
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Cited by 3 (1 self)
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In this paper we propose an object grammar decomposition for the classes of columnconvex, and directed columnconvex polyominoes. As a consequence, we obtain the enumeration of such classes according to the semiperimeter, thus giving a natural explanation of the fact that the generating
The Number of Convex Polyominoes and the Generating Function of Jacobi Polynomials
, 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 ..."
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Cited by 3 (3 self)
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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
, 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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Cited by 2 (0 self)
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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
Random generation of Qconvex sets
"... The problem of randomly generating Qconvex sets is considered. We present two generators. The first one uses the Qconvex hull of a set of random points in order to generate a Qconvex 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 Qconvex sets is considered. We present two generators. The first one uses the Qconvex hull of a set of random points in order to generate a Qconvex 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
 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. ..."
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Cited by 7 (3 self)
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. The final goal of the paper is to determine the generating function of convex polyominoes according to the semiperimeter, and it is achieved by applying an idea introduced in [11].
Enumeration of Symmetry Classes of Convex Polyominoes on the Honeycomb Lattice
, 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 ..."
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Cited by 3 (0 self)
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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
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366