Partitions with ``d(a) copies of a''
type: Item
instance of: scholarly article
title: Partitions with ``d(a) copies of a''
zbMATH Open document ID: 0653.05005
DOI: 10.1016/0097-3165(88)90079-9
author: A. K. Agarwal
author: Gary L. Mullen
published in: Journal of Combinatorial Theory. Series A
publication date: 1988-01-01T00:00:00Z
review text: In an earlier paper, \textit{A. K. Agarwal} and \textit{G. E. Andrews} [J. Comb. Theory, Ser. A 45, 40-49 (1987; Zbl 0618.05003)] discussed Rogers- Ramanujan identities for partitions with ``a copies of a''. The authors in the present paper study a class of partitions using d(a) copies of each part a, where d(a) represents the number of positive divisors of a. Several results including combinatorial identities, a generating function, a recursive formula, an asymptotic formula, and a graphical representation for these newly introduced partitions are given in the paper. Also, an identity for partitions with ``d(a) copies of a'' analogous to the identity considered, for instance, in [Can. J. Math. 34, 194-195 (1982; Zbl 0482.10013)] and [J. Comb. Theory, Ser. A 36, 249-252 (1984; Zbl 0532.05003)] are given. The paper concludes by posing several open problems.
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 4064991
zbMATH Keywords: conjugate partitions
zbMATH Keywords: two-color partitions
zbMATH Keywords: self-conjugate-partitions
zbMATH Keywords: identities for partitions
zbMATH Keywords: generating function
zbMATH Keywords: recursive formula
zbMATH Keywords: asymptotic formula
zbMATH Keywords: graphical representation
reviewed by: Ravinder Krishna Raina
MaRDI profile type: Publication
full work available at URL: 0097-3165(88)90079-9
OpenAlex ID: W2067703703
cites work: Q3748283
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description: scientific article; zbMATH DE number 4064991