Exhaustive generation of gominoes

In this paper, we consider the generation of three classes of polyominoes, distinguished by their connectivity type. We present a two-player game called gomino, and we show how this game induces an algorithm to generate these sets of polyominoes according to their site-perimeter. We then use a variation of the gomino algorithm to obtain exact expressions for the number of polyominoes inscribed in a rectangle of size b×k with area bk−r, where r≤5.