An extremal problem on the set of noncoprime divisors of a number

P. Erdős, M. Herzog, J. Schönheim

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

A combinatorial theorem is established, stating that if a family A1, A2, …, As of subsets of a set M contains every subset of each member, then the complements in M of the A’s have a permutation C1, C2, …, Cs such that Ci ⊃Ai. This is used to determine the minimal size of a maximal set of divisors of a number N no two of them being coprime.

Original languageEnglish
Pages (from-to)408-412
Number of pages5
JournalIsrael Journal of Mathematics
Volume8
Issue number4
DOIs
Publication statusPublished - 1970

Fingerprint

Extremal Problems
Divisor
Subset
Coprime
Permutation
Complement
Theorem
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

An extremal problem on the set of noncoprime divisors of a number. / Erdős, P.; Herzog, M.; Schönheim, J.

In: Israel Journal of Mathematics, Vol. 8, No. 4, 1970, p. 408-412.

Research output: Contribution to journalArticle

Erdős, P. ; Herzog, M. ; Schönheim, J. / An extremal problem on the set of noncoprime divisors of a number. In: Israel Journal of Mathematics. 1970 ; Vol. 8, No. 4. pp. 408-412.
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