TY - JOUR

T1 - An extremal problem on the set of noncoprime divisors of a number

AU - Erdös, P.

AU - Herzog, M.

AU - Schönheim, J.

PY - 1970/12

Y1 - 1970/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=1842752541&partnerID=8YFLogxK

U2 - 10.1007/BF02798688

DO - 10.1007/BF02798688

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AN - SCOPUS:1842752541

SN - 0021-2172

VL - 8

SP - 408

EP - 412

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 4

ER -