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

Pedro H. Milet, Nicolau C. Saldanha

Published 2014-04-25, updated 2014-11-02Version 2

We investigate tilings of cubiculated regions with two simply connected floors by 2 x 1 x 1 bricks. More precisely, we study the flip connected component for such tilings, and provide an algebraic invariant that "almost" characterizes the flip connected components of such regions, in a sense that we discuss in the paper. We also introduce a new local move, the trit, which, together with the flip, connects the space of domino tilings when the two floors are identical.