Ordering minimum-phase sets: Numerical properties and systematic searches

The main property of the ordered minimum-phase (OMP) sets is that they can be ordered as minimum-phase sequences. Several theoretical properties of such sets are already known. Amongst them, the set of all points having OMP property is an open non empty set. In this paper we present some numerical properties of the OMP sets, which may lead to systematic and fast exploration of permutations, in order to discover the OMP sets. Both are using lists of permutations: in the first case we have the most appropriate permutations list, in the second case we use a tabu-list of permutations.