1,721,017 research outputs found
Polyominoes determined by permutations: enumeration via bijections
No full textA permutominide is a set of cells in the plane satisfying special connectivity constraints and uniquely defined by a pair of permutations. It naturally generalizes the concept of permutomino, recently investigated by several authors and from different points of view [1, 2, 4, 6, 7]. In this paper, using bijective methods, we determine the enumeration of various classes of convex permutominides, including, parallelogram, directed convex, convex, and row convex permutominides. As a corollary we have a bijective proof for the number of convex permutominoes, which was still an open problem
On the equivalence problem for succession rules
No full textThe notion of succession rule (system for short) provides a powerful tool for the enumeration of many classes of combinatorial objects. Often, different systems exist for a given class of combinatorial objects, and a number of problems arise naturally. An important one is the equivalence problem between two different systems. In this paper, we show how to solve this problem in the case of systems having a particular form. More precisely, using a bijective proof, we show that the classical system defining the sequence of Catalan numbers is equivalent to a system obtained by linear combinations of labels of the first one
An object grammar for column-convex polyominoes
No full textIn 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 of both the classes are algebraic
Fighting fish
No full textWe introduce new combinatorial structures, called fighting fish, that generalize directed convex polyominoes by allowing them to branch out of the plane into independent substructures. On the one hand the combinatorial structure of fighting fish appears to be particularly rich: we show that their generating function with respect to the perimeter and number of tails is algebraic, and we conjecture a mysterious multivariate equidistribution property with the left ternary trees introduced by Del Lungo et al On the other hand, fighting fish provide a simple and natural model of random branching surfaces which displays original features: in particular, we show that the average area of a uniform random fighting fish with perimeter 2n is of order n 5/4: to the best of our knowledge this behaviour is non-standard and suggests that we have identified a new universality class of random structures
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
The number of Z-convex polyominoes
No full textIn 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). This class of convex polyominoes appears to resist standard decompositions, so we propose a construction by “inflation” that allows to write a system of functional equations for their generating functions. The generating function P(t) of Z-convex polyominoes with respect to the semi-perimeter turns out to be algebraic all the same and surprisingly, like the generating function of convex polyominoes, it can be expressed as a rational function of t and the generating function of Catalan numbers
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