Abstract

We study the problem of tiling a rectangular p×n-strip (p N fixed, n N) with pieces, i.e., sets of simply connected cells. Some well-known examples are strip tilings with dimers (dominoes) and/or monomers. We prove, in a constructive way, that every tiling problem is equivalent to a regular grammar, that is, the set of possible tilings constitutes a regular language. We propose a straightforward algorithm to transform the tiling problem into its corresponding grammar. By means of some standard methods, we are then able to obtain some counting generating functions that are rational. We go on to give some examples of our method and indicate some of its applications to a number of problems treated in current literature.