MacMahon's Partition Analysis XI: Broken diamonds and modular forms

George E. Andrews; Peter Paule

doi:10.4064/aa126-3-5

MacMahon's Partition Analysis XI: Broken diamonds and modular forms

George E. Andrews
, Peter Paule

Research Institute for Symbolic Computation

Research output: Contribution to journal › Article › peer-review

Abstract

MacMahon developed Partition Analysis as a calculational and analytic method to produce the generating functions for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of MacMahon's original project. One of the key results obtained with Partition Analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.

Original language	English
Pages (from-to)	281-294
Number of pages	14
Journal	Acta Arithmetica
Volume	126
Issue number	3
DOIs	https://doi.org/10.4064/aa126-3-5
Publication status	Published - 2007

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

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abstract = "MacMahon developed Partition Analysis as a calculational and analytic method to produce the generating functions for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of MacMahon's original project. One of the key results obtained with Partition Analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.",

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AB - MacMahon developed Partition Analysis as a calculational and analytic method to produce the generating functions for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of MacMahon's original project. One of the key results obtained with Partition Analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.

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DO - 10.4064/aa126-3-5

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JF - Acta Arithmetica

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MacMahon's Partition Analysis XI: Broken diamonds and modular forms

Abstract

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