Combinatoric enumeration of two-dimensional proper arrays Original Research Article

An image proper array is a two-dimensional rectangular array composed of directed cubes that obey certain constraints. Because of these constraints, the image proper arrays may be classified via a schema in which each image proper array is associated with a particular image column. For a fixed n, the goal is to enumerate, modulo symmetry, all possible edge configurations associated with image proper arrays. By varying n, one constructs four combinatoric sequences, each of which enumerates a particular class of edge configurations. Convolution arguments and resultant calculations associate these sequences with cubic equations. These cubic equations allow one to predict image, the number of edge configurations, modulo symmetry, associated with image proper arrays.