A coloring invariant for ribbon LL-tetrominos

We investigate tiling problems for regions in a square lattice by ribbon LL-shaped tetrominoes. Our results show that tiling of the first quadrant by ribbon LL-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 LL-shaped tetrominoes.