Infinite Sidon sequences
Number Theory
2013-05-16 v2 Combinatorics
Abstract
We present a new method to obtain infinite Sidon sequences, based on the discrete logarithm. We construct an infinite Sidon sequence A, with A(x)= x^{\sqrt 2-1+o(1)}. Ruzsa proved the existence of a Sidon sequence with similar counting function but his proof was not constructive. Our method generalizes to B_h sequences: For all h\ge 3, there is a B_h sequence A such that A(x)=x^{\sqrt{(h-1)^2+1}-(h-1)+o(1)}.
Cite
@article{arxiv.1209.0326,
title = {Infinite Sidon sequences},
author = {Javier Cilleruelo},
journal= {arXiv preprint arXiv:1209.0326},
year = {2013}
}
Comments
Corrected typos and revised arguments, results unchanged