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Density Inequalities for Sets of Multiples

✍ Scribed by Rudolf Ahlswede; Levon H. Khachatrian

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
274 KB
Volume
55
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

For tinite sets (A, B \subset \mathbb{N}), the set of positive integers, consider the set least common multiples ([A, B]={[a, b]: a \in A, b \in B}), the set of largest common divisors ((A, B)={(a, b): a \in A, b \in B}). the set of products (A \times B={a, b: a \in A, b \in B}). and the sets of their multiples (M(A)=A \times \mathbb{N}, M(B), M[A, B], M(A, B)), and (M(A \times B)). resp. Our discoveries are the inequalities

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