``Integer-making'' theorems
type: Item
instance of: scholarly article
title: ``Integer-making'' theorems
zbMATH Open document ID: 0473.05046
DOI: 10.1016/0166-218X(81)90022-6
author: József Beck
author: Tibor Fiala
published in: Discrete Applied Mathematics
publication date: 1981-01-01T00:00:00Z
review text: Let \(f(n)=\max |\sum_{i\in E} (a_i-\alpha_i)|\) with \(a_i\) integer, \(\alpha_i\) real and \(| a_i-\alpha_i|<1\) for all \(i\), where the maximum is taken over all finite sets \(E\) having maximum degree \(n\). The authors prove that \(f(n)<n-1\) for \(n\geq 2\) (and conjecture that \(f(n)<c\sqrt n\)). A similar result (and also a similar conjecture) is given for another such function.
reviewed by: T. Spircu
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 90C10
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 3741444
zbMATH Keywords: subsets
MaRDI profile type: Publication
cites work: Q4063504
cites work: On a combinatorial game
cites work: Balancing families of sets
Wikidata QID: Q56456690
description: scientific article; zbMATH DE number 3741444