The mysterious story of square ice, piles of cubes, and bijections.
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- Record sourced from PubMed, PMID 32879007.
- Also identified by DOI 10.1073/pnas.2005525117 and PMC identifier 7519258.
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Abstract
When combinatorialists discover two different types of objects that are counted by the same numbers, they usually want to prove this by constructing an explicit bijective correspondence. Such proofs frequently reveal many more details about the relation between the two types of objects than just equinumerosity. A famous set of problems that has resisted various attempts to find bijective proofs for almost 40 y is concerned with alternating sign matrices (which are equivalent to a well-known physics model for two-dimensional ice) and their relations to certain classes of plane partitions. In this paper we tell the story of how the bijections were found.