Even partition functions
type: Item
instance of: scholarly article
title: Even partition functions
zbMATH Open document ID: 1042.11008
published in: Séminaire Lotharingien de Combinatoire
publication date: 2003-07-07T00:00:00Z
full work available at URL: https://eudml.org/doc/123676
review text: For a set \(A\) of positive integers, \(p(A,n)\) denotes the number of partitions of \(n\) into parts from \(A\). Given an integer \(N\) and a set \(B \subset \{1, 2, .., N\}\) one easily sees that there is a unique set \(A\) such that \(A \bigcap [1,N] = B\) and \(p(A,n)\) is even for \(n>N\). Initially it was believed that such sets are completely irregular. This paper shows that, on the contrary for \(N=3\) and \(B=\{1,2,3\}\) the corresponding set \(A\) has a rich multiplicative structure. Elements of \(A\) are composed exclusively of primes congruent to 3, 5 or 6 modulo 7 (except 2 and 7), and within such numbers there are further conditions to determine membership in \(A\). Based on this, the authors are able to prove that the cardinality of \(A\) up to \(x \) is asymptotic to \( c x ( \log x)^{-3/4}\).
Mathematics Subject Classification ID: 11B34
Mathematics Subject Classification ID: 11P83
zbMATH DE Number: 1889085
author: Fethi Ben Saïd
author: Jean-Louis Nicolas
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1889085