Virtual Library

Papers and reprints relevant to our research

Alternating sign matrices and domino tilings, Elkies-Kuperberg-Larsen-Propp
A well-known research paper detailing topics very similar to what we are researching. Download Now
Counting constrained domino tilings of Aztec diamonds, Gessel-Ionescu-Propp
Contains several proofs utilizing the domino shuffling algorithm that allow one to obtain accurate information about the typical behavior of large, randomly tiled Aztec diamonds. Download Now
Generalized domino shuffling, Propp
Explains three algorithms that are useful for different calculations on a randomly tiled Aztec Diamond. Download Now
Wikipedia article on Dodgson condensation
Method for calculating determinants of nxn matrices discovered by Lewis Carol (James Dodgson). Go to Site
Dodgson condensation and alternating sign matrices, Hone
This paper explains in detail the bijection between Dodgson condensation and alternating sign matrices. Download Now
Applications of graphical condensation for enumerating matchings and tilings, Kuo
Graphical condensation involves superimposing matchings of a graph onto matchings of a smaller subgraph, and then re-partitioning the united matching (actually a multigraph) into matchings of two other subgraphs, in one of two possible ways. This technique can be used to enumerate perfect matchings of a wide variety of planar bipartite graphs. Download Now
Alternating sign matrices and descending plane partitions, Mills-Robbins-Rumsey
Contains a brief overview of alternating sign matrices and descending plane partitions, and several conjectures and theorems about them are presented. Download Now
Excerpts from Cox-Little-O'Shea pertaining to quotient ideals
A couple examples that show what exactly quotient ideals are, and how they are useful in our field of study. First Page Second Page
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