On a calculus of partition functions

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The main object in this paper is to show that many partition theorems which have been deduced from identities in basic hypergeometric series and infinite products may in fact be given purely combinatorial proofs. We show that the manipulations performed on the generating functions have combinatorial interpretations, and thus we obtain a “calculus of partition functions” which translates a sizable portion of the techniques of the elementary theory of basic hypergeometric series into arithmetic terms.

Original languageEnglish (US)
Pages (from-to)555-562
Number of pages8
JournalPacific Journal of Mathematics
Volume31
Issue number3
DOIs
StatePublished - Dec 1969

Fingerprint

Basic Hypergeometric Series
Partition Function
Calculus
Infinite product
Generating Function
Manipulation
Partition
Term
Theorem
Interpretation
Object

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "The main object in this paper is to show that many partition theorems which have been deduced from identities in basic hypergeometric series and infinite products may in fact be given purely combinatorial proofs. We show that the manipulations performed on the generating functions have combinatorial interpretations, and thus we obtain a “calculus of partition functions” which translates a sizable portion of the techniques of the elementary theory of basic hypergeometric series into arithmetic terms.",
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On a calculus of partition functions. / Andrews, George E.

In: Pacific Journal of Mathematics, Vol. 31, No. 3, 12.1969, p. 555-562.

Research output: Contribution to journalArticle

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