3D Dimer Block Party

Come play with 250 physical wooden blocks and join us in thinking about a simple open problem for dimers in 3D. No prior knowledge required. We’ll start with an ~10 minute presentation explaining the problem and then suggest some things for everyone to try to construct with the blocks.

A bit more detail: a dimer tiling of a region R contained in Z^d is a tiling by blocks which are length 2 in one dimension and length 1 in all others (e.g. like dominos in 2D or like bricks in 3D). In 2D, there is a local move called a flip (a flip takes two parallel tiles and rotates them, e.g. || becomes = ). It turns out that any two dimer tilings of the same simply connected planar region are connected by a sequence of flips. In 3D, dimer tilings are not connected under flips even on the 3x3x2 box. Adding another local move called a trit involving 3 tiles instead of 2, it’s an open question whether dimer tilings of the LxNxM box are connected under flips and trits if L,M,N > 2.