Treffer: A New Upper Bound for B2[2] Sets: A new upper bound for \(B_2 [2]\) sets
Title:
A New Upper Bound for B2[2] Sets: A new upper bound for \(B_2 [2]\) sets
Authors:
Source:
Journal of Combinatorial Theory, Series A. 93:378-384
Publisher Information:
Elsevier BV, 2001.
Publication Year:
2001
Subject Terms:
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
0097-3165
DOI:
10.1006/jcta.2000.3084
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....b3c6658945dca2f2193cc942b0b38500
Database:
OpenAIRE
Weitere Informationen
A \(B_2[g]\) set \({\mathcal A}\) is a set of integers such that, for any integer \(n\), \(|\{(a_1,a_2),a_i\in{\mathcal A},\;a_1+a_2=n,\;a_1\leq a_2\}|\leq g\). Thus \(B_2[1]\) sets are Sidon sets. It was shown by \textit{J. Cilleruelo} [ibid. 89, 141--144 (2000; Zbl 0955.11005)] that if \({\mathcal A}\) is a \(B_2 [2]\) set in \(\{1,\dots,N\}\), then \(|{\mathcal A}|\leq(6N)^{1/2}+1\). The present author improves this result, showing that, for sufficiently large \(N\), \(|{\mathcal A}|\leq 2.363584\sqrt N\).