Maximal upper asymptotic density of sets of integers with missing differences from a given set

Title:

Maximal upper asymptotic density of sets of integers with missing differences from a given set

Creator:

Pandey, Ram Krishna

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:96e97dc1-27a1-4bb7-8b6c-23523af0451a
uuid:96e97dc1-27a1-4bb7-8b6c-23523af0451a
doi:10.21136/MB.2015.144179

Subject:

upper asymptotic density and maximal density

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let M be a given nonempty set of positive integers and S any set of nonnegative integers. Let δ(S) denote the upper asymptotic density of S. We consider the problem of finding µ(M) := sup S δ(S), where the supremum is taken over all sets S satisfying that for each a, b ∈ S, a − b ∉ M. In this paper we discuss the values and bounds of µ(M) where M = {a, b, a + nb} for all even integers and for all sufficiently large odd integers n with a < b and gcd(a, b) = 1.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

53-69

Source:

Mathematica bohemica | 2015 Volume:140 | Number:1

Harvested from:

CDK

Metadata only:

false