Double tangent method for two-periodic Aztec diamonds

Aztec Diamonds and Baxter Permutations

Abstract We present a proof of a conjecture about the relationship between Baxter permutations and pairs of alternating sign matrices that are produced from domino tilings of Aztec diamonds. It is shown that a tiling corresponds to a pair of ASMs that are both permutation matrices if and only if the larger permutation matrix corresponds to a Baxter permutation. There has been a thriving literat...

Aztec Diamonds, Checkerboard Graphs, and Spanning Trees

This note derives the characteristic polynomial of a graph that represents nonjump moves in a generalized game of checkers. The number of spanning trees is also determined.

Domino Shuffling on Novak Half-Hexagons and Aztec Half-Diamonds

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 ...

Higher Dimensional Aztec Diamonds and a (2d + 2)-Vertex Model

Motivated by the close relationship between the number of perfect matchings of the Aztec diamond graph introduced in [5] and the free energy of the square-ice model, we consider a higher dimensional analog of this phenomenon. For d ≥ 2, we construct d-uniform hypergraphs which generalize the Aztec diamonds and we consider a companion d-dimensional statistical model (called the 2d +2-vertex mode...

On Domino Tilings of Rectangles Aztec Diamonds in the Rough