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Journal of the London Mathematical Society Advance Access published online on November 14, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm079
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© 2007 London Mathematical Society

MacMahon's partition analysis XII: plane partitions

George E. Andrews

Department of Mathematics
The Pennsylvania State University
University Park
PA 16802
USA
andrews{at}math.psu.edu

Peter Paule

Research Institute for Symbolic Computation (RISC )
Johannes Kepler University
4040 Linz
Austria

MacMahon developed partition analysis as a calculational and analytic method to produce the generating function 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 our retrieval 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.

2000 Mathematics Subject Classification 05A17 (primary), 05A15, 05E99, 11P81 (secondary).

The first author was partially supported by NSF grant DMS-0457003. The second author was partially supported by SFB grant F1305 of the Austrian FWF.

Received August 16, 2006;
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