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 language | English (US) |
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Pages (from-to) | 555-562 |
Number of pages | 8 |
Journal | Pacific Journal of Mathematics |
Volume | 31 |
Issue number | 3 |
DOIs | |
State | Published - Dec 1969 |
All Science Journal Classification (ASJC) codes
- General Mathematics