Dense infinite $B_h$ sequences

Abstract

For $h=3$ and $h=4$ we prove the existence of infinite $B_h$ sequences $\B$ with counting function $$\mathcal{B}(x)=x^{\sqrt{(h-1{)}^2+1}-(h-1)+o(1)}.$$ This result extends a construction of I. Ruzsa for $B_2$ sequences.

We have organized the contents in a different way and we have extended the theorem to B_4 sequences

References in corpus (1)

• A remark of Ruzsa's construction of an infinite Sidon set