A congruence for \(c{\varphi{}}_{h,k}(n)\)
type: Item
instance of: scholarly article
title: A congruence for \(c{\varphi{}}_{h,k}(n)\)
zbMATH Open document ID: 0766.11042
author: Louis W. Kolitsch
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-05-16T00:00:00Z
review text: Let \(c\varphi_{h,k}(n)\) be the number of generalized Frobenius partitions of \(n\) with \(h\) colors and at most \(k\) repetitions, as introduced by \textit{Padmavathamma} [Fibonacci Q. 27, 125-130 (1989; Zbl 0669.10025)]. It is proved that \[ \sum_{d\mid(h,n)} \mu(d) c\varphi_{h/d,k}(n/d)\equiv 0\pmod{hH}, \] where \(H\) is the product of all the prime power factors of \(h\) which are relatively prime to \(k+1\). As an immediate corollary, \[ \sum_{d\mid(h,n)}\mu(d)c\varphi_{h/d,k}(n/d)\equiv 0\pmod h^ 2 \] if \((h,k+1)=1\).
Mathematics Subject Classification ID: 11P83
zbMATH DE Number: 168037
zbMATH Keywords: congruence
zbMATH Keywords: generalized Frobenius partitions
zbMATH Keywords: colors
zbMATH Keywords: repetitions
reviewed by: Betty Garrison
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072705
OpenAlex ID: W1980885871
cites work: An extension of a congruence by Andrews for generalized Frobenius partitions
cites work: Q3822240
cites work: Q3822242
DOI: 10.1216/RMJM/1181072705
description: scientific article; zbMATH DE number 168037