From Aztec diamonds to pyramids: Steep tilings

On Domino Tilings of Rectangles Aztec Diamonds in the Rough

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...

Domino Tilings of Aztec Diamonds, Baxter Permutations, and Snow Leopard Permutations∗

In 1992 Elkies, Kuperberg, Larsen, and Propp introduced a bijection between domino tilings of Aztec diamonds and certain pairs of alternating-sign matrices whose sizes differ by one. In this paper we first study those smaller permutations which, when viewed as matrices, are paired with the matrices for doubly alternating Baxter permutations. We call these permutations snow ∗2010 AMS Subject Cla...

A Simple Proof for the Number of Tilings of Quartered Aztec Diamonds

In this paper a (lattice) region is a connected union of unit squares in the square lattice. A domino is the union of two unit squares that share an edge. A (domino) tiling of a region R is a covering of R by dominos such that there are no gaps or overlaps. Denote by T(R) the number of tilings of the region R. The Aztec diamond of order n is defined to be the union of all the unit squares with ...

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.