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Sets of Integers with Missing Differences

✍ Scribed by Soma Gupta

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 133 KB
Volume: 89
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3003

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✦ Synopsis

This paper deals with the problem of finding the maximal density, +(M), of sets of integers in which differences given by a set M do not occur. The problem is solved for the case where the elements of M are in arithmetic progression. Besides finding lower bounds for most members of the general three element set M, +(M ) has been found for most members of the family [i, j, k], where iÂd#jÂd (mod 2) and gcd(i, j )=d. For iÂd jÂd (mod 2) and gcd(i, j )=d it is conjectured that the lower bound found is the best possible. A lower bound is given for +(M) for the set M=[i, j, i+ j] and +(M ) for certain infinite families of four element set M have been found.

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