SIDON SETS IN A UNION OF INTERVALS

We study the maximum size of Sidon sets in unions of integer intervals. If A subset of N is the union of two intervals and if vertical bar A vertical bar = n (where vertical bar A vertical bar denotes the cardinality of A), we prove that A contains a Sidon set of size at least 0,876 root n. On the other hand, by using the small differences technique, we establish a bound of the maximum size of Sidon sets in the union of k intervals.