Flip invariance for domino tilings of three-dimensional regions with two floors (Q2351026)

The authors investigate tilings of three-dimensional cubiculated regions of special kind (so-called two-story regions and their particular case duplex regions) by dominoes, which are \(2 \times 1 \times 1\) bricks. A flip is a local move which is a natural generalization of the two-dimensional flip for domino tilings. In the paper, the authors study the connected components of the above regions by flips. They introduce a polynomial invariant which in some sense characterizes the connected components by flips. A new local move, the trit, is introduced and it is proved that the space of domino tilings of a duplex region is connected by flips and trits. Also, the authors discuss the situation when tilings of duplex regions are embedded in large regions.