A coloring invariant for ribbon -tetrominos

We investigate tiling problems for regions in a square lattice by ribbon L -shaped tetrominoes. Our results show that tiling of the first quadrant by ribbon L -tetrominoes is possible only if it reduces to a tiling by 2×4 and 4×2 rectangles. A consequence is the description of all rectangles that can be tiled by ribbon L -shaped tetrominoes.