From the 1 of 4 linked papers with an AI index.
4 papers
Dimers, filters, and -deformed real numbers
James Propp
The paper introduces a q‑parameterized function [[x]]_q for each positive real number x by constructing an inhomogeneous dimer model (equivalently, a filter model on a poset) and s…
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…