Infinite Sidon sequences
نویسنده
چکیده
We give the first explicit construction of an infinite Sidon sequence A with A(x) x for some c > 1/3. Our method allows to take c = √ 2− 1. Ruzsa proved the existence of a Sidon sequence with similar counting function but his proof was not constructive. Our method generalizes to Bh sequences when h ≥ 3. In these case our constructions are not explicit but they give the first improvements on the trivial lower bounds for these sequences: for all h ≥ 3, there is a Bh sequence A such that A(x) = x √ (h−1)2+1−(h−1)+o(1).
منابع مشابه
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تاریخ انتشار 2013