A circulant is a Cayley graph of a cyclic group Arc transitive circulants of square free order are classi ed It is shown that an arc transitive circulant of square free order n is one of the following the lexicographic product Kb or the deleted lexicographic Kb b where n bm and is an arc transitive circulant or is a normal circulant that is Aut has a normal regular cyclic subgroup

We introduce a new global constraint which combines together a lexicographic ordering constraint with some sum constraints. Applications for this constraint include balanced incomplete block designs and the ternary Steiner problem. We develop an efficient linear time algorithm for propagating this constraint. This combination of constraints increases the filtering, leading to significant decrea...

Integer programming has many applications in economics and management. Applying lexicographic ordering and linear programming, we develop an iterative method for integer programming, which defines an increasing mapping from a finite lattice into itself. Given any polytope, within a finite number of iterations, the method either yields an integer point in the polytope or proves no such point exi...