On a calculus of partition functions

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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.

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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