Domino shuffling on Novak half-hexagons and Aztec half-diamonds (Q640439)

Summary: We explore the connections between the well-studied Aztec Diamond graphs and a new family of graphs called the Half-Hexagons, discovered by Jonathan Novak. In particular, both families of graphs have very simple domino shuffling algorithms, which turn out to be intimately related. This connection allows us to prove an ``arctic parabola'' theorem for the Half-Hexagons as a corollary of the Arctic Circle theorem for the Aztec Diamond.