منابع مشابه
Parallelogram Polyominoes and Corners
(Received) We give an equation satissed by the generating function for parallelogram polyominoes according to the area, the width and the number of left path corners. Next, we give an explicit formula for the generating function of these polyominoes according to the area, the width and the number of right and left paths corners.
متن کاملCombinatorics of labelled parallelogram polyominoes
We obtain explicit formulas for the enumeration of labelled parallelogram polyominoes. These are the polyominoes that are bounded, above and below, by northeast lattice paths going from the origin to a point (k, n). The numbers from 1 to n (the labels) are bijectively attached to the n north steps of the above-bounding path, with the condition that they appear in increasing values along consecu...
متن کاملParallelogram polyominoes, the sandpile model on a bipartite graph, and a q, t-Narayana polynomial
In this talk I will highlight some results from a recent paper (arXiv:1208.0024) that was motived by a correspondence between bivincular permutation patterns and composition matrices. We study recurrent configurations of the sandpile model on the complete bipartite graph Km,n and show how they can be classified in terms of a class of polyominoes. A canonical toppling process on these recurrent ...
متن کاملAnisotropic step, mutual contact and area weighted festoons and parallelogram polyominoes on the triangular lattice
We present results for the generating functions of polygons and more general objects that can touch, constructed from two fully directed walks on the infinite triangular lattice, enumerated according to each type of step and weighted proportional to the area and the number of contacts between the directed sides of the objects. In general these directed objects are known as festoons, being const...
متن کاملSlicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciled
We provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schröder and Baxter generalizations of parallelogram polyominoes (called slicings) which grow according to these succession rules. We also exhibit Schröder subclasses of Baxter classes, namely a Schröder subset o...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1995
ISSN: 0747-7171
DOI: 10.1006/jsco.1995.1062