On a theorem of Alladi and Gordon and the Gaussian polynomials
type: Item
instance of: scholarly article
title: On a theorem of Alladi and Gordon and the Gaussian polynomials
zbMATH Open document ID: 0854.05009
DOI: 10.1016/0097-3165(95)90112-4
author: Christine Bessenrodt
published in: Journal of Combinatorial Theory. Series A
publication date: 1997-01-05T00:00:00Z
review text: By analyzing a continued fraction of Ramanujan, the reviewer and \textit{B. Gordon} [J. Comb. Theory, Ser. A 63, No. 2, 275-300 (1993; Zbl 0781.05006)] obtained a general partition identity in the form of an equality between three partition functions \(A\), \(B\) and \(C\). This generalized earlier results due to Bressoud and Göllnitz. The reviewer and Gordon established the equality \(A= C\) combinatorially by constructing a bijective, but to prove \(A= B\) they utilized Ramanujan's continued fraction. In this paper, the author constructs an explicit bijection between \(A\) and \(B\). In doing so, not only a strong refinement of the Alladi-Gordon theorem is obtained, but some new insights into certain Gaussian polynomial formulas are revealed.
reviewed by: Krishnaswami Alladi
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P81
zbMATH DE Number: 720832
zbMATH Keywords: levels
zbMATH Keywords: colored parts
zbMATH Keywords: partition
zbMATH Keywords: Alladi-Gordon theorem
zbMATH Keywords: Gaussian polynomial
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90112-4
OpenAlex ID: W2049804290
cites work: Partition identities and a continued fraction of Ramanujan
cites work: On the Geometry of Numbers in Elementary Number Theory
cites work: Identities in combinatorics. III: Further aspects of ordered set sorting
cites work: Bijective proofs of basic hypergeometric series identities
description: scientific article; zbMATH DE number 720832