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Structure Theorem for Multiple Addition and the Frobenius Problem

✍ Scribed by Vsevolod F. Lev

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
304 KB
Volume
58
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let A [0; l] be a set of n integers, and let h 2. By how much does |hA| exceed |(h&1) A| ? How can one estimate |hA| in terms of n, l ? We give sharp lower bounds extending and generalizing the well-known theorem of Freiman for |2A|. A number of applications are provided as well. In particular, we give a solution for the old extremal problem of Frobenius Erdo s Graham concerning estimating of the largest integer, non-representable by a linear form. In a sense, our solution can not be improved.

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