On the asymptotic behaviour of general partition functions
type: Item
instance of: scholarly article
title: On the asymptotic behaviour of general partition functions
zbMATH Open document ID: 1010.11059
DOI: 10.1023/A:1009821821206
published in: The Ramanujan Journal
publication date: 2002-10-20T00:00:00Z
review text: If \(N\) is the set of all natural numbers, \(n\in N\), and \(A \subset N\), let \(p_A(n)\) denote the number of partitions of \(n\) such that all parts belong to \(A\); likewise let \(q_A(n)\) denote the number of partitions of \(n\) into distinct parts belonging to \(A\). The authors prove four asymptotic results, one of which is as follows: Theorem 1: For every infinite set \(A\subset N\), we have \[ \limsup_{n \to\infty} {\log\biggl( \max \bigl(2,p_A(n) \bigr)\biggr) \over\log \biggl(\max \bigl(2,q_A(n) \bigr)\biggr)} \geq\sqrt 2. \] The other results require additional assumptions on \(A\).
Mathematics Subject Classification ID: 11P82
zbMATH DE Number: 1455275
zbMATH Keywords: number of partitions
zbMATH Keywords: asymptotic results
author: Jean-Louis Nicolas
author: András Sárközy
reviewed by: Neville Robbins
MaRDI profile type: Publication
full work available at URL: a:1009821821206
OpenAlex ID: W4247238579
description: scientific article; zbMATH DE number 1455275