Density sets of sets of positive integers

On a Density for Sets of Integers

A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the introduced density are derived.

Periodic Sets of Integers

On a Class of Densities of Sets of Positive Integers

A method proposed by R. Alexander in his paper published in Acta Arithmetica XII (1967) enables to obtain various densities of set of positive integers, including asymptotic and logarithmic ones. In our paper some properties of the above mentioned densities are studied and certain earlier results on the asymptotic and logarithmic density are strengthened. Introduction and notations In what foll...

The Least Common Multiple of Random Sets of Positive Integers

We study the typical behavior of the least common multiple of the elements of a random subset A ⊂ {1, . . . , n}. For example we prove that lcm{a : a ∈ A} = 2n(1+o(1)) for almost all subsets A ⊂ {1, . . . , n}.

On additive partitions of sets of positive integers

Consider any set U = (u,,} with elements defined by u,, +? = u,, +, + u,,, n z 1, where u, and u2 are relatively prime positive integers. We show that if u, Cu, or 2 ( u,uz, then the set of positive integers can be partitioned uniquely into two disjoint sets such that the sum of any two distinct memhers of any one set is never in U. If U,>LQ and 21 u,uz. no such partition is possible. Further r...