On exceptional systems of random integers
type: Item
instance of: scholarly article
title: On exceptional systems of random integers
zbMATH Open document ID: 0849.11054
author: Bruce Love
author: Jean Pedersen
author: Peter Hilton
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1996-06-24T00:00:00Z
full work available at URL: https://eudml.org/doc/225897
review text: The paper deals with the following problem: Let \(n_1, n_2, \dots, n_k\) be positive integers and let \(X_1, X_2, \dots, X_k\) be stochastically independent random integers such that \(X_j\) is uniformly distributed on the set \(\{1, \dots, n_j\}\) for \(j= 1, \dots, k\). A system \((n_1, n_2, \dots, n_k, m)\) is said to be \(u\)-good iff \[ P \Biggl( \sum^k_{j=1} X_j \equiv u\bmod m \Biggr)= {1\over m} \qquad \text{for} \quad 0\leq u\leq m-1. \] Some characterizations of such systems to be \(u\)-good are given. Furthermore, several cases are discussed.
Mathematics Subject Classification ID: 11K31
Mathematics Subject Classification ID: 11A07
Mathematics Subject Classification ID: 60B99
zbMATH DE Number: 817248
zbMATH Keywords: exceptional systems
zbMATH Keywords: uniform distribution
zbMATH Keywords: frequency
zbMATH Keywords: sporadic systems
zbMATH Keywords: \(u\)-good systems
zbMATH Keywords: random integers
reviewed by: Lothar Heinrich
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 817248