Publications of Paul Erdos

Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No: 518.10063
Autor: Erdös, Paul; Freud, R.; Hegyvari, N.
Title: Arithmetical properties of permutations of integers. (In English)
Source: Acta Math. Hung. 41, 169-176 (1983).
Review: Let a₁,...,a_n be a permutation of 1,...,n and let [a_i,a_j] denote the least common multiple of a_i and a_j. It is shown that

maxmax_{1 \leq i < n}[a_i,a_i+1] = (1+o(1))\frac{n²}{4 log n},

where the minimum is taken over all permutations. This result is best possible since in any permutation there must be an a_i such that [a_i,a_i+1] \geq (1+o(1))\frac{n²}{4 log n}. It is also shown that there is an infinite permutation a₁,a₂,... of the positive integers such that

[a_i,a_i+1] < ie^{c\sqrt{log i} log log i}

for all i. Some results are also obtained for the greatest common divisor. See also following review.
Reviewer: I.Anderson
Classif.: * 11B05 Topology etc. of sets of numbers
                   11A05 Multiplicative structure of the integers
                   11B75 Combinatorial number theory
                   05A05 Combinatorial choice problems
Keywords: permutations; density of sums; least common multiple; greatest common divisor
Citations: Zbl.518.10064

Books Problems Set Theory Combinatorics Extremal Probl/Ramsey Th.

Graph Theory Add.Number Theory Mult.Number Theory Analysis Geometry

Probabability Personalia About Paul Erdös Publication Year Home Page

Books	Problems	Set Theory	Combinatorics	Extremal Probl/Ramsey Th.
Graph Theory	Add.Number Theory	Mult.Number Theory	Analysis	Geometry
Probabability	Personalia	About Paul Erdös	Publication Year	Home Page