Counting profile strings from rectangular tilings
Anthony Petrosino, Alissa Schembor, Kathryn Haymaker · Involve a Journal of Mathematics · 2020
We study the enumeration of profiles, which are outlines that occur when tiling a rectangular board with squares, dominoes, and trominoes. Profiles of length [math] correspond to a special subset of the set [math] , called profile strings. Profiles and their corresponding strings first appeared in the enumeration of the tilings of rectangular [math] and [math] boards with squares, dominoes, and trominoes. Profiles also play a role in enumerating the tilings of an [math] board for any fixed [math] . We describe how profiles arise when enumerating tilings, and we prove that the number of profile strings of length [math] equals [math] .