Given a planar domain on the rectangular grid, how many ways are there of tiling it by dominos (that is, by 1x2 rectangles)? And how does a generic tiling of a given domain look like?

It turns out that these questions are related to the determinants-based formulas, and that likewise formulas appear in many similar situations. In this direction, one obtains the famous arctic circle theorem, describing the behaviour of a generic domino tiling of an aztec diamond, and a statement for the lozenges tilings on the hexagonal lattice, giving the shape of a corner of a cubic crystal.