Random Sidon sequences
type: Item
instance of: scholarly article
title: Random Sidon sequences
zbMATH Open document ID: 0924.11006
author: Anant P. Godbole
author: Svante Janson
author: Nicholas W. jun. Locantore
author: Rebecca Rapoport
published in: Journal of Number Theory
publication date: 1999-05-26T00:00:00Z
review text: Consider a subset \(A\) chosen randomly from the \( n \choose k_n\) subsets of size \(k_n\) of \([1, 2,\dots, n]\). The paper investigates the probability that such a set has the \(B_h\) property, that is, whether the sums of \(h\) elements of \(A\) are all distinct. It is proved that if \(k_n/n^{1/2h} \rightarrow \Lambda \) as \(n \rightarrow \infty \), then this probability tends to \( \exp \bigl( -\kappa _h \Lambda ^{2k} \bigr) \) with certain positive constants \(\kappa _h\). In particular, if \(k_n/n^{1/2h} \rightarrow 0\), then almost all sets have the \(B_h\) property, and if \(k_n/n^{1/2h} \rightarrow \infty \), then almost all do not have it. The proofs are based on Janson's inequality and the Stein-Chen approximation for positively related random variables.
Mathematics Subject Classification ID: 11B13
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 1274808
zbMATH Keywords: Sidon sets
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
OpenAlex ID: W2064598807
cites work: Q4004078
cites work: Q4002919
cites work: On sums of a Sidon-sequence
cites work: Q4885319
cites work: Q3963072
cites work: An inequality for B2-sequences
cites work: Q4895030
cites work: Q4845262
DOI: 10.1006/JNTH.1998.2325
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description: scientific article; zbMATH DE number 1274808