We consider several new families of subgraphs of the square grid whose matchings are enumerated by powers of several small prime numbers: 2, 3, 5, and 11. Our graphs are obtained by trimming two opposite corners of an Aztec rectangle. The result yields a proof of a conjecture posed by Ciucu. In addition, we reveal a hidden connection between our graphs and the hexagonal dungeons introduced by B...

ion of the floc and simplifying hypothesis Next we will develop a 2D model of the floc, using some simplifying hypothesis. Our model is hybrid, since it uses concepts from individual based models, as developed by Delft school, together with classical ones. Based on experimental evidences, collected with FISH based techniques, we assume that the developing floc will have the generic dimensions L...

In many industrial and non-industrial applications, it is necessary to identify the largest inscribed rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for finding the largest axis aligned inscribed rectangle in a general polygon. ...

Let P be a set of n objects on a square grid. A push is a transformation of P that involves sweeping a horizontal or vertical line by one unit, starting from the hull of P , displacing objects in the direction of the sweep. For example, when pushing to the right, all the leftmost objects are displaced one unit to the right. This in turn displaces other objects further right. Given P , we want t...

The Ginzburg-Landau equations we study arise in the modeling of superconductivity. One widely used method of discretizing the equations together with the associated periodic boundary conditions, in the case of a rectangle of dimension 2, leads to a ve-point stencil. Solving the system means inverting a sparse matrix of dimension N 2 , where N is the number of grid points on each side of the rec...

The quality and life of pavement is greatly affected by the type of sub-grade, sub base and base course materials. The most important of these are the type and quality of sub-grade soil. But in India most of the flexible pavements are need to be constructed over weak and problematic sub-grade. The California bearing ratio (CBR) of these sub-grade have very low, it needs to more thickness of pav...

In this paper, we present CoMRI, Compressed MultiResolution Index, our system for fast sequence similarity search in DNA sequence databases. We employ Virtual Bounding Rectangle (VBR) concept to build a compressed, grid style index structure. An advantage of grid format over trees is subsequence location information is given by the order of corresponding VBR in the VBR list. Taking advantage of...

We show that each quadrangulation on n vertices has a closed rectangle of influence drawing on the (n − 2) × (n − 2) grid. Further, we present a simple algorithm to obtain a straight-line drawing of a quadrangulation on the ⌈ n 2 ⌉ × ⌈ 3n 4 ⌉ grid. This is not optimal but has the advantage over other existing algorithms that it is not needed to add edges to the quadrangulation to make it 4-conn...

A visibility drawing of a plane graph G is a drawing of G where each vertex is drawn as a horizontal line segment and each edge is drawn as a vertical line segment such that the line segments use only grid points as their endpoints. The area of a visibility drawing is the area of the smallest rectangle on the grid which encloses the drawing. A minimum-area visibility drawing of a plane graph G ...