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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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The number of smallest parts in the partitions of n

George E. Andrews1

1 The Pennsylvania State University, University Park, PA 16802, USA. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2008, Issue 624, Pages 133–142, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2008.083, October 2008

Publication History

Received:
2007-06-22
Revised:
2007-07-31
Published Online:
2008-10-29

Abstract

We denote by spt(n) the total number of appearances of the smallest part in each integer partition of n. We shall relate spt(n) to the Atkin-Garvan moments of ranks, and we shall prove that 5 | spt(5n + 4), 7 | spt(7n + 5) and 13 | spt(13n + 6).

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