ISLANDS: FROM CODING THEORY TO ENUMERATIVE COMBINATORICS AND TO LATTICE THEORY - OVERVIEW AND OPEN PROBLEMS.

As a tool to characterize instantaneous codes, Foldes and Singhi determined the maximum number of certain subsets of the set of the first n natural numbers in 2006. This motivated Czédli in 2009 to determine the maximum number of the analogous subsets of a rectangular grid. He called these subsets islands. The present paper summarizes recent results on this topic. [ABSTRACT FROM AUTHOR]