Papers on Tilings of Aztec Diamonds

Alternating-Sign Matrices and Domino Tilings, by Noam Elkies, Greg Kuperberg, Michael Larsen, and Jim Propp, Journal of Algebraic Combinatorics 1 (1992), 111-132 and 219-234.

Random Domino Tilings and the Arctic Circle Theorem, by William Jockusch, Jim Propp, and Peter Shor.

Local Statistics for Random Domino Tilings of the Aztec Diamond, by Henry Cohn, Noam Elkies, and Jim Propp, Duke Mathematical Journal 85 (1996), 117-166.

Edge effects on local statistics in lattice dimers: a study of the Aztec diamond finite case, by Harald Helfgott (Brandeis Universty bachelor's thesis, 1998).

Papers on Generating Random Tilings

Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics, by Jim Propp and David Wilson, Random Structures and Algorithms 9 (1996), 223-252.

Arctic Behavior in Random Tilings, by Matthew Blum.

Miscellaneous Papers

An Illustrative Study of the Enumeration of Tilings: Conjecture Discovery and Proof Techniques by Chris Douglas. (For the original bare-bones version, see A Proof of Jim Propp's Power of Two Conjecture by Chris Douglas.)

Twenty Open Problems in Enumeration of Matchings by Jim Propp, and the companion Progress Report.

Counting Tilings of Subgraphs of Aztec Diamonds by Ben Wieland.

Two and Three Dimensional Young Diagrams by Matthew Blum.

A Test of the Universality Conjecture by Ruth Britto-Pacumio.

An Alternative Technique for Proving the Aztec Diamond Theorem and Other Applications by Eric Kuo. (For the original bare-bones version, see New proof that the number of tilings for an Aztec diamond is 2^(n(n+1)/2) by Eric Kuo.)

Jim Propp's rough write-up of the "urban renewal" method.

The grant proposal that convinced the National Science Foundation and the National Security Agency to pay for all this.

Documentation relating to our software

For documentation, click here.

Return to the UROP home page.