1. Introduction. A Sidon set is a set A of integers with the property that all the sums a+b, a,b∈ A, a≤b are distinct. A Sidon set A⊂ [1,N] can have as many as (1+o(1))√N elements, hence N/2 sums. The distribution of these sums is far from arbitrary. Erdős, Sárközy and T. Sós [1,2] established several properties of these sumsets. Among other things, in [2] they prove that A + A cannot contain an interval longer than C√N, and give an example that is possible. In [1] they show that A + A contains gaps longer than clogN, while the maximal gap may be of size O(√N). We improve these bounds. In Section 2, we give an example of A + A containing an interval of length c√N; hence in this question the answer is known up to a constant factor. In Section 3, we construct A such that the maximal gap is . In Section 4, we construct A such that the maximal gap of A + A is O(logN) in a subinterval of length cN.
@article{bwmeta1.element.bwnjournal-article-aav77i4p353bwm,
author = {Imre Z. Ruzsa},
title = {Sumsets of Sidon sets},
journal = {Acta Arithmetica},
volume = {76},
year = {1996},
pages = {353-359},
zbl = {0872.11013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav77i4p353bwm}
}
Imre Z. Ruzsa. Sumsets of Sidon sets. Acta Arithmetica, Tome 76 (1996) pp. 353-359. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav77i4p353bwm/
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