Domino shuffling on Novak half-hexagons and Aztec half-diamonds

Understand

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.