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

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

2011-03-25

arxiv.org/abs/1103.5054v1

Mathematics

Combinatorics

20 Pages, 7 Figures

Scientific paper

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.

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