Analytic study of norms of prime partitions
type: Item
instance of: scholarly article
title: Analytic study of norms of prime partitions
zbMATH Open document ID: 1489.11161
author: A. Kumar
published in: Bulletin des Sciences Mathématiques
publication date: 2021-08-17T00:00:00Z
review text: Considering an ordinary partition of the positive integer \(n\), the product of its parts is called the norm of the partition as suggested by \textit{R. Schneider} and \textit{A. V. Sills} [Integers 20A, Paper A13, 16 p. (2020; Zbl 1458.11144)]. Prime partitions are partitions of integers into prime parts. For their number, see \textit{R. C. Vaughan} [Ramanujan J. 15, No. 1, 109--121 (2008; Zbl 1154.11035)]. In the paper under review the author studies norms of prime partitions. Let \(r_p(i, n)\) denote the number of times \(i\) appears as a norm in the prime partitions of \(n\). The author gives the generating function of \(r_p(i, n)\) with consequences and recursive relations on certain weighted sums on \(r_p(i, n)\) too.
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11A41
Mathematics Subject Classification ID: 11A51
zbMATH DE Number: 7382526
zbMATH Keywords: norm of a partition
zbMATH Keywords: prime partitions
zbMATH Keywords: semiprimes
reviewed by: Mihály Szalay
describes a project that uses: OEIS
MaRDI profile type: Publication
full work available at URL: j.bulsci.2021.103038
OpenAlex ID: W3191223792
cites work: Arithmetic of partitions and the $q$-bracket operator
cites work: Partition zeta functions
cites work: The product of parts or "norm" of a partition
cites work: Q4965425
cites work: Q5395427
cites work: Q5246240
cites work: On the number of partitions into primes
cites work: Inductive formulas related to prime partitions
cites work: Q5246238
cites work: Q4443440
cites work: Q3801620
cites work: Q5272741
cites work: On the number of prime factors of summands of partitions
DOI: 10.1016/J.BULSCI.2021.103038
description: scientific article; zbMATH DE number 7382526