Alejandro Erickson Durham A domino tatami covering is a classical domino tiling in which no 4 dominoes meet. This local restriction of the (polynomial time) question, “Can the region R be covered with dominoes?” is NP-complete, and I give a reduction from planar 3SAT, using a SAT-solver to construct the gadgets. In the second half of the talk I introduce monominoes, and I describe the tatami structure. I use this to enumerate certain coverings of the n x n square, confirming something first observed to by Don Knuth. This is joint work with Frank Ruskey