We study the enumeration of profiles, which are outlines that occur when tiling a rectangular board with squares, dominoes, and trominoes. Profiles of length correspond to a special subset of the set , called profile strings. Profiles and their corresponding strings first appeared in the enumeration of the tilings of rectangular and boards with squares, dominoes, and trominoes. Profiles also play a role in enumerating the tilings of an board for any fixed . We describe how profiles arise when enumerating tilings, and we prove that the number of profile strings of length equals .
"Counting profile strings from rectangular tilings." Involve 13 (5) 861 - 870, 2020. https://doi.org/10.2140/involve.2020.13.861