Abstract
We shall provide an account of MacMahon’s development of a calculational, analytic method designed to produce the generating function for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly 20 years finding an alternative treatment. This paper provides an account of our retrieval of MacMahon’s original dream of using Partition Analysis to treat plane partitions in general.
Mathematics Subject Classification: Primary: 05A17; Secondary:05A15, 05E99, 11P81
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Acknowledgements
We thank Christian Krattenthaler for pointing out that substitution (5) we found with Partition Analysis leads us to rediscover Gansner’s theorem.
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Andrews, G.E., Paule, P. (2012). MacMahon’s Dream. In: Alladi, K., Garvan, F. (eds) Partitions, q-Series, and Modular Forms. Developments in Mathematics, vol 23. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0028-8_1
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