Journal ArticleDOI
A Combinatorial Proof of the Triple Product Identity
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This article is published in American Mathematical Monthly.The article was published on 1984-08-01. It has received 17 citations till now. The article focuses on the topics: Identity (philosophy) & Combinatorial proof.read more
Citations
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Journal ArticleDOI
Partition bijections, a survey
TL;DR: In this article, an extensive survey of bijective proofs of classical partitions identities is presented, and various extensions and generalizations are added in the form of exercises; see Section 2.
Journal ArticleDOI
The quintuple product identity
TL;DR: A comprehensive survey of the work on the quintuple product identity, and a detailed analysis of the many proofs are given.
Journal ArticleDOI
Uniform proofs of q-Series-product identities
TL;DR: In this paper, a simple proof of the Jacobi triple product identity by using basic properties of cube roots of unity was given, and some new product identities were derived by this uniform method.
Book ChapterDOI
The Triple, Quintuple and Septuple Product Identities Revisited
Dominique Foata,Guo-Niu Han +1 more
TL;DR: The Jacobi triple and Watson quintuple identities have been derived combinatorially in several manners in the classical literature, e.g. as mentioned in this paper, and the Farkas-Kra septuple product identity has been shown to be a combinatorial identity.
Journal ArticleDOI
The generating functions of the rank and crank modulo 8
TL;DR: In this paper, the number of partitions of n with rank (Dyson) congruent to i (mod m) and M(j,m,n) with crank (Andrews, Garvan) is given.
References
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Book
An Introduction to the Theory of Numbers
TL;DR: The fifth edition of the introduction to the theory of numbers has been published by as discussed by the authors, and the main changes are in the notes at the end of each chapter, where the author seeks to provide up-to-date references for the reader who wishes to pursue a particular topic further and to present a reasonably accurate account of the present state of knowledge.
Journal ArticleDOI
A Rogers-Ramanujan bijection
TL;DR: It appears that the methods given lead to an algorithm for constructing bijections for other identities of Rogers-Ramanujan type such as the Gordon identities.