On a calculus of partition functions

George E. Andrews

Vol. 31 (1969), No. 3, 555–562

DOI: 10.2140/pjm.1969.31.555

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.

Mathematical Subject Classification

Primary: 05.10

Secondary: 10.00

Milestones

Received: 5 May 1969

Published: 1 December 1969