Tromino tilings of domino-deficient rectangles

In this paper I have settled the open problem, posed by J. Marshall Ash and S. Golomb in [4], of tiling an m × n rectangle with L-shaped trominoes, with the condition that 3 |(mn 2) and a domino is removed from the given rectangle. It turns out that for any given m, n ≥ 7, the only pairs of squares which prevent a tiling are {(1,2), (2,2)}, {(2,1), (2,2)}, {(2,3), (2,4)}, {(3,2), (4,2)} and their symmetric counterparts. For all other cases, the existence of a tiling is shown. Some results on tiling the general case of 2-deficiency are also discussed.