Construction of Non-expandable Non-overlapping Sets of Pictures

TL;DR

This paper introduces a method to construct non-expandable non-overlapping sets of pictures, extending the concept of cross-bifix-free string sets to two dimensions, with potential applications demonstrated.

Contribution

The paper presents a novel construction method for non-expandable non-overlapping sets of pictures, generalizing existing string-based concepts to two-dimensional images.

Findings

Constructed explicit examples of NENO sets

Proved non-expandability of the constructed sets

Discussed potential applications of these sets

Abstract

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 present a construction of non-expandable non-overlapping (NENO) sets of pictures and show some examples of application.