Recursive formulae for the multiplicative partition function
type: Item
instance of: scholarly article
title: Recursive formulae for the multiplicative partition function
zbMATH Open document ID: 0923.11142
DOI: 10.1155/S0161171299222132
author: Jun Kyo Kim
author: Sang Geun Hahn
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1999-10-31T00:00:00Z
full work available at URL: https://eudml.org/doc/48258
review text: The identity \[ np(n)=\sum^n_{k=1} \sigma(k)p (n-k) \] is well-known. Using elementary means, the authors prove an analogous identity involving partitions of multi-partite numbers. They use this identity to correct some erroneous results given long ago by MacMahon. A couple of errors appear on the first page; for example, \((1,0)+(1,0)+ (1,0)\) should be \((1,0)+ (1,0)+(0,1)\); \(f(12)p(2,1)\) should be \(f(12)=p(2,1)\).
Mathematics Subject Classification ID: 11P82
zbMATH DE Number: 1275575
zbMATH Keywords: recursive formulae
zbMATH Keywords: multiplicative partition function
zbMATH Keywords: identities
zbMATH Keywords: partitions of multi-partite numbers
reviewed by: Neville Robbins
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1275575