Abstract: We study tilings of regions in the square lattice with L-shaped trominoes. Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where it either remains NP-complete or has a polynomial time algorithm. First, we characterize the possibility of when an Aztec rectangle and an Aztec diamond has an L-tromino tiling. Then, we study tilings of arbitrary regions where only $180^\circ$ rotations of L-trominoes are available. For this particular case we ...
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Topics: 
Combinatorics
Discrete mathematics