Consider lattice paths in Z 2 with three step types: the up diagonal (1; 1), the down diagonal (1; ?1), and the double horizontal (2; 0). For n 1, let S n denote the set of such paths running from (0; 0) to (2n; 0) and remaining strictly above the x-axis except initially and terminally. It is well known that the cardinalities, r n = jS n j, are the large Schrr oder numbers. We use lattice paths...

We provide mechanisms that facilitate database design based on a shrink wrap schema. A shrink wrap schema is a well-crafted, complete, global schema that represents an application. We develop the notion of concept schemas as a way to decompose shrink wrap schemas. A concept schema is a subset of an application schema that addresses one particular point of view in an application. To aid in shrin...

Finding shortest paths and shortest distances between points on a surface S in three-dimensional space is a well-studied problem in differential geometry and computational geometry. The shortest path between two points on S is denoted a geodesic path on the surface and the shortest distance between two points on S is denoted a geodesic distance. In this survey, we consider the case where a disc...