In the context of combinatorial sampling, so-called “unranking method” can be seen as a link between total order over objects and an effective way to construct object given rank. The most classical used in this is lexicographic order, which corresponds familiar word ordering dictionary. article, we propose comparative study four algorithms dedicated unranking combinations, including three that ...

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...