"Integer-making" theorems

József Beck, Tibor Fiala

Research output: Contribution to journalArticlepeer-review

178 Scopus citations

Abstract

Let X = {x1, x2,...} be a finite set and associate to every xi a real number αi. Let f(n) [g (n)] be the least value such that given any family F of subsets of X having maximum degree n [cardinality n], one can find integers αi, i=1,2,... so that αi - αi|<1 and ∑ xi ε{lunate} Eai- ∑ xi ε{lunate} Eαi≤f{hook}(n) ∑ xi ε{lunate} Eai- ∑ xi ε{lunate} Eαi≤g(n) for all E ε{lunate} F. We prove f(n)≤n - 1 and g(n)≤c(n log n) 1 2.

Original languageEnglish (US)
Pages (from-to)1-8
Number of pages8
JournalDiscrete Applied Mathematics
Volume3
Issue number1
DOIs
StatePublished - Feb 1981
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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