Affiliation:
1. Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
Abstract
In one of their recent collaborative papers, Andrews and Paule continue their study of partition functions via MacMahon's Partition Analysis by considering partition functions associated with directed graphs which consist of chains of diamond shape. They prove a congruence related to one of these partition functions and conjecture a number of similar congruence results. In this note, we reprove this congruence by constructing an explicit way to group partitions. Then we keep the essence of the method and manage to apply it to a different kind of plane partitions to get more general results and several other congruences.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Reference4 articles.
1. The Encyclopedia of Mathematics and Its Applications Series;Andrews G. E.,1976
2. MacMahon's partition analysis XI: Broken diamonds and modular forms
3. P. A. MacMahon, Combinatory Analysis 2 (Cambridge Univ. Press, Cambridge) pp. 1915–1916.
Cited by
13 articles.
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