Annals of Combinatorics 4 (2000) 327-338

MacMahon's Partition Analysis: II  Fundamental Theorems

George E. Andrews

Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

Received April 21, 1999

AMS Subject Classification: 05A17, 05A19, 05A30, 11P81

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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