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Random Domino Tilings and the Arctic Circle Theorem
William Jockusch, James Propp, Peter Shor
In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in…
Whirling injections, surjections, and other functions between finite sets
Michael Joseph, James Propp, Tom Roby
This paper analyzes a certain action called "whirling" that can be defined on any family of functions between two finite sets equipped with a linear (or cyclic) ordering. Many maps…
Lattice structure for orientations of graphs
James Propp
In 1986, Oliver Pretzel studied the set of orientations of a connected finite graph and showed that any two such orientations having the same flow-difference around all closed…
Some 2-adic conjectures concerning polyomino tilings of Aztec diamonds
James Propp
For various sets of tiles, we count the ways to tile an Aztec diamond of order using tiles from that set. The resulting function often has interesting behavior when one…