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Annals of Combinatorics

, Volume 4, Issue 3–4, pp 327–338 | Cite as

MacMahon's Partition Analysis: II Fundamental Theorems

  • George E. Andrews

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.

Keywords: Partition Analysis, partitions, plane partitions 

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Copyright information

© Birkhäuser Verlag Basel, 2000

Authors and Affiliations

  • George E. Andrews
    • 1
  1. 1.Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA, e-mail: andrews@math.psu.eduUS

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