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MacMahon's Partition Analysis: II Fundamental Theorems

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Abstract.

We continue the study of the method outlined by MacMahon in Section VIII of [10]. The long range object is to show the relevance of MacMahon's ideas in current partition-theoretic research. In this paper we present a number of theorems which MacMahon overlooked. For example, the number of partitions of n with non-negative first and second differences between parts equals the number of partitions of n into triangular numbers.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA, e-mail: andrews@math.psu.edu, , , , , , US

    George E. Andrews

Authors
  1. George E. Andrews

Additional information

Received April 21, 1999

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Andrews, G. MacMahon's Partition Analysis: II Fundamental Theorems. Annals of Combinatorics 4, 327–338 (2000). https://doi.org/10.1007/PL00001284

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  • DOI: https://doi.org/10.1007/PL00001284