Non-expandable non-overlapping sets of pictures

The non-overlapping sets of pictures are sets such that no two pictures in the set (properly) overlap. They are the generalization to two dimensions of the cross-bifix-free sets of strings. Non-overlapping sets of pictures are non-expandable when no other picture can be added without violating the property. We propose a general construction method for non-expandable non-overlapping (NENO) sets based on some structural properties of NENO sets. As an application, we show a first example of a family of NENO sets.