  Configurations are necklaces with prescribed numbers of red and black beads.
Among all possible configurations, the regular one plays an important role in
many applications. In this paper, several aspects of regular configurations are
discussed, including construction, uniqueness, symmetry group and the link with
balanced words.
  Another model of configurations is the polygons formed by a given number of
sides of two different lengths. In this context, regular configurations are
used to obtain a lower bound for the cycles packing number of shift graphs, a
subclass of the directed circulant graphs.
