Refinements and generalizations of Capparelli's conjecture on partitions
type: Item
instance of: scholarly article
title: Refinements and generalizations of Capparelli's conjecture on partitions
zbMATH Open document ID: 0830.05005
author: Krishnaswami Alladi
author: George E. Andrews
author: Basil Gordon
published in: Journal of Algebra
publication date: 1995-08-13T00:00:00Z
review text: Caparelli's conjecture asserts the equality of the number of \(C\)- partitions and the number of \(D\)-partitions of \(n\) where a \(C\)-partition is a partition into distinct parts not congruent to \(\pm 1\) modulo 6 and a \(D\)-partition is one in which the difference between parts is at least 4 unless two parts are both divisible by 3 or add up to a multiple of 3, in which case they may differ by as little as 2. Various proofs of this conjecture now exist. This paper proves a generalization with four additional parameters which, for \(D\)-partitions, keep track of the number of parts in each residue class modulo 3 and of \(\lceil (\ell+ 2)/3\rceil\) where \(\ell\) is the largest part. Several different proofs are given.
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 783881
zbMATH Keywords: Caparelli's conjecture
zbMATH Keywords: partition
Wikidata QID: Q105723284
reviewed by: David M. Bressoud
MaRDI profile type: Publication
full work available at URL: jabr.1995.1144
OpenAlex ID: W1997343040
DOI: 10.1006/JABR.1995.1144
description: scientific article; zbMATH DE number 783881