منابع مشابه
Quadrant Marked Mesh Patterns
In this paper we begin the first systematic study of distributions of quadrant marked mesh patterns. Mesh patterns were introduced recently by Brändén and Claesson in connection with permutation statistics. Quadrant marked mesh patterns are based on how many elements lie in various quadrants of the graph of a permutation relative to the coordinate system centered at one of the points in the gra...
متن کاملCoincidence among families of mesh patterns
Two mesh patterns are coincident if they are avoided by the same set of permutations. In this paper, we provide necessary conditions for this coincidence, which include having the same set of enclosed diagonals. This condition is sufficient to prove coincidence of vincular patterns, although it is not enough to guarantee coincidence of bivincular patterns. In addition, we provide a generalizati...
متن کاملQuadrant Marked Mesh Patterns in Alternating Permutations
Abstract. This paper is a continuation of the systematic study of the distribution of quadrant marked mesh patterns initiated by the authors in [J. Integer Sequences 12 (2012), Article 12.4.7]. We study quadrant marked mesh patterns on up-down and down-up permutations, also known as alternating and reverse alternating permutations, respectively. In particular, we refine classical enumeration re...
متن کاملHarmonic numbers, Catalan's triangle and mesh patterns
The notion of a mesh pattern was introduced recently, but it has already proved to be a useful tool for description purposes related to sets of permutations. In this paper we study eight mesh patterns of small lengths. In particular, we link avoidance of one of the patterns to the harmonic numbers, while for three other patterns we show their distributions on 132-avoiding permutations are given...
متن کاملFast Mesh Interpolation and Mesh Expansion with Applications
A fast iterative method for constructing a smooth subdivision surface that interpolates the vertices of an arbitrary mesh is presented. The construction is done by iteratively adjusting vertices of the given mesh locally until control mesh of the required interpolating surface is reached. The new interpolation method not only has the simplicity of local methods, but also has the capability of g...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2013
ISSN: 0196-8858
DOI: 10.1016/j.aam.2013.08.002