Generating functions for column-convex polyominoes
نویسندگان
چکیده
منابع مشابه
Consecutive Patterns: From Permutations to Column-Convex Polyominoes and Back
We expose the ties between the consecutive pattern enumeration problems as sociated with permutations, compositions, column-convex polyominoes, and words. Our perspective allows powerful methods from the contexts of compositions, column convex polyominoes, and of words to be applied directly to the enumeration of per mutations by consecutive patterns. We deduce a host of new consecutive patt...
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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...
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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 ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1988
ISSN: 0097-3165
DOI: 10.1016/0097-3165(88)90071-4